Number Fusion • Lesson • Lenny.com
Number Fusion A rigorous Grade 7 math lesson focused on computing fluently with decimals, fractions, and mixed numbers. Students master foundational multi-digit decimal operations, mixed-number arithmetic, combined decimal-fraction problem-solving, and realistic multi-step applications.
CS Chynna Smith
Number Fusion Practice Workbook
A comprehensive three-page Grade 7 math practice workbook featuring 6 problems for each operation (addition, subtraction, multiplication, division) under decimals, mixed numbers, and mixed representations (72 problems total) with dedicated student work boxes.
Number Fusion Answer Key
A comprehensive three-page master teacher answer key corresponding to the Number Fusion Practice Workbook, providing final answers, worked algebraic/arithmetic steps, and dual decimal-fraction solutions for all 72 problems.
Decimal Operations Reference Sheet
A comprehensive single-page reference sheet and anchor chart for Grade 7 decimal operations, illustrating step-by-step algorithms, visual examples, place value benchmarks, and common pitfalls for addition, subtraction, multiplication, and division.
Number Fusion A rigorous Grade 7 math lesson focused on computing fluently with decimals, fractions, and mixed numbers. Students master foundational multi-digit decimal operations, mixed-number arithmetic, combined decimal-fraction problem-solving, and realistic multi-step applications.
CS Chynna Smith
Number Fusion Practice Workbook Grade 7 Mathematics • Topic 1 of 3
Number Fusion: Decimal Operations
Name:
Date:
Score: / 24
Fluency Protocol: 6 Problems per Operation Align decimal points vertically. Show computation in each work box.
Addition (+)
Subtraction (-)
Multiplication (×)
Division (÷)
\( 12.4 + 15.3 \)
Ans:
\( 34.68 + 21.57 \)
Ans:
\( 14.85 + 29.376 \)
Ans:
\( 8.094 + 17.65 \)
Ans:
\( 142.7 + 68.495 \)
Ans:
\( 0.875 + 19.468 + 3.2 \)
Ans:
\( 28.75 - 13.42 \)
Ans:
\( 64.2 - 27.8 \)
Ans:
\( 45.3 - 18.76 \)
Ans:
\( 52.1 - 27.684 \)
Ans:
\( 100.0 - 43.875 \)
Ans:
\( 81.04 - 39.678 \)
Ans:
\( 4.2 \times 3.5 \)
Ans:
\( 6.8 \times 0.4 \)
Ans:
\( 3.45 \times 2.8 \)
Ans:
\( 12.6 \times 0.75 \)
Ans:
\( 0.36 \times 0.45 \)
Ans:
\( 15.24 \times 3.05 \)
Ans:
\( 15.6 \div 3 \)
Ans:
\( 28.8 \div 0.6 \)
Ans:
\( 21.45 \div 1.5 \)
Ans:
\( 18.72 \div 0.24 \)
Ans:
\( 7.56 \div 1.8 \)
Ans:
\( 3.825 \div 0.85 \)
Ans:
Number Fusion Practice • Topic 1: Decimals Page 1 of 3 Turn page for Mixed-Number Operations →
Grade 7 Mathematics • Topic 2 of 3
Number Fusion: Mixed-Number Operations
Name:
Date:
Score: / 24
Fluency Protocol: 6 Problems per Operation Find common denominators or improper forms. Reduce to simplest form.
Addition (+)
Subtraction (-)
Multiplication (×)
Division (÷)
\( 2\frac{1}{4} + 3\frac{2}{4} \)
Ans:
\( 4\frac{1}{3} + 2\frac{1}{6} \)
Ans:
\( 3\frac{3}{4} + 2\frac{5}{6} \)
Ans:
\( 5\frac{2}{5} + 1\frac{7}{10} \)
Ans:
\( 6\frac{5}{8} + 4\frac{3}{4} \)
Ans:
\( 7\frac{2}{3} + 5\frac{4}{5} \)
Ans:
\( 5\frac{5}{6} - 2\frac{1}{6} \)
Ans:
\( 6\frac{7}{8} - 3\frac{1}{4} \)
Ans:
\( 5\frac{1}{4} - 2\frac{3}{4} \)
Ans:
\( 7\frac{1}{3} - 4\frac{5}{8} \)
Ans:
\( 8\frac{2}{5} - 3\frac{7}{10} \)
Ans:
\( 10 - 4\frac{3}{7} \)
Ans:
\( 1\frac{1}{2} \times 2\frac{2}{3} \)
Ans:
\( 2\frac{1}{4} \times 1\frac{1}{3} \)
Ans:
\( 2\frac{2}{5} \times 1\frac{7}{8} \)
Ans:
\( 3\frac{1}{5} \times 2\frac{1}{2} \)
Ans:
\( 4\frac{2}{3} \times 1\frac{2}{7} \)
Ans:
\( 3\frac{3}{8} \times 2\frac{2}{9} \)
Ans:
\( 3\frac{1}{2} \div 1\frac{3}{4} \)
Ans:
\( 4\frac{2}{3} \div 1\frac{1}{6} \)
Ans:
\( 2\frac{5}{8} \div 1\frac{3}{4} \)
Ans:
\( 5\frac{1}{3} \div 2\frac{2}{3} \)
Ans:
\( 3\frac{3}{5} \div 1\frac{1}{5} \)
Ans:
\( 6\frac{2}{5} \div 3\frac{1}{5} \)
Ans:
Number Fusion Practice • Topic 2: Mixed Numbers Page 2 of 3 Turn page for Mixed Representations →
Grade 7 Mathematics • Topic 3 of 3
Number Fusion: Mixed Representations
Name:
Date:
Score: / 24
Fluency Protocol: 6 Problems per Operation Convert forms to either pure decimals or fractions before computing.
Addition (+)
Subtraction (-)
Multiplication (×)
Division (÷)
\( 4.5 + 2\frac{1}{4} \)
Ans:
\( 5.4 + 3\frac{1}{4} \)
Ans:
\( 3\frac{3}{5} + 4.65 \)
Ans:
\( 1.375 + 2\frac{1}{2} \)
Ans:
\( 6\frac{7}{10} + 5.84 \)
Ans:
\( 2\frac{3}{8} + 7.125 \)
Ans:
\( 7.8 - 3\frac{1}{2} \)
Ans:
\( 6\frac{1}{2} - 2.85 \)
Ans:
\( 8.25 - 4\frac{3}{5} \)
Ans:
\( 9\frac{3}{4} - 5.625 \)
Ans:
\( 10.4 - 6\frac{4}{5} \)
Ans:
\( 5\frac{1}{8} - 2.75 \)
Ans:
\( 2\frac{1}{2} \times 0.6 \)
Ans:
\( 2\frac{4}{5} \times 1.5 \)
Ans:
\( 3.2 \times 1\frac{1}{4} \)
Ans:
\( 4\frac{1}{2} \times 0.8 \)
Ans:
\( 1\frac{3}{5} \times 2.25 \)
Ans:
\( 0.75 \times 3\frac{1}{3} \)
Ans:
\( 4.8 \div 1\frac{1}{5} \)
Ans:
\( 7.2 \div 1\frac{1}{5} \)
Ans:
\( 6\frac{1}{4} \div 2.5 \)
Ans:
\( 5.4 \div 2\frac{1}{4} \)
Ans:
\( 8\frac{2}{5} \div 1.4 \)
Ans:
\( 3\frac{3}{4} \div 0.5 \)
Ans:
Number Fusion Practice • Topic 3: Mixed Representations Page 3 of 3 Complete all 72 problems • Show full mathematical thinking
Number Fusion Answer Key Teacher Scoring Key • Topic 1 Solutions
Decimal Operations: Answer Key
Page 1: 24 Pts 1 pt each
Grading Criteria: 0.5 pt algorithmic step / place value alignment + 0.5 pt correct final value Accept equivalent trailing zeros (e.g. 9.66 = 9.660)
Addition (+)
Subtraction (-)
Multiplication (×)
Division (÷)
\( 12.4 + 15.3 \)
Tenths aligned:
No carry 27.7
\( 34.68 + 21.57 \)
Regroup 10ths & 100ths:
Regrouping 56.25
\( 14.85 + 29.376 \)
Pad 0: 14.850
Pad zero 44.226
\( 8.094 + 17.65 \)
Align thousandths:
Thousandths 25.744
\( 142.7 + 68.495 \)
Pad zeros:
Large addends 211.195
\( 0.875 + 19.468 + 3.2 \)
3 addends aligned:
3 values 23.543
\( 28.75 - 13.42 \)
Direct subtraction:
Standard 15.33
\( 64.2 - 27.8 \)
Borrow 1 whole (10 tenths):
Regroup 36.4
\( 45.3 - 18.76 \)
Write 45.30:
Zero padding 26.54
\( 52.1 - 27.684 \)
Borrow across zeros:
Across 0s 24.416
\( 100.0 - 43.875 \)
100.000 - 43.875:
From 100 56.125
\( 81.04 - 39.678 \)
81.040 - 39.678:
Internal 0 41.362
\( 4.2 \times 3.5 \)
\( 42 \times 35 = 1470 \)
2 dec. 14.7
\( 6.8 \times 0.4 \)
\( 68 \times 4 = 272 \)
2 dec. 2.72
\( 3.45 \times 2.8 \)
\( 345 \times 28 = 9660 \)
Decimal Operations Reference Sheet Quick Reference Anchor Sheet • Grade 7 Mathematics
Decimal Operations Reference Guide
Keep in Math Binder Core Rules • Worked Examples • Pitfalls
Decimal Place Values
Hundreds 100
Tens 10
Ones 1
Point •
Tenths 0.1
Hundredths 0.01
Thousandths 0.001
Addition: Line Up the Dots
Rule 1
Line up the decimal points vertically.Pad empty spaces with placeholder zeros.Add right to left , regrouping as needed.Bring the decimal point straight down.
Example: \( 14.85 + 29.376 \) Aligned
14.850
+ 29.376
44.226
-
Subtraction: Line Up & Pad
Rule 2
Line up decimal points with larger value on top.MUST pad zeros on the top number to subtract.Borrow/regroup across place values carefully.Bring decimal point straight down into difference.
Example: \( 52.1 - 27.684 \) Must Pad Zeros
52.100
- 27.684
24.416
×
Multiplication: Count & Slide
Rule 3
DO NOT line up decimals! Multiply like whole numbers.Count total decimal places in BOTH factors.Slide decimal point in product from right to left that exact total number of places.
Example: \( 3.45 \times 2.8 \) 2 + 1 = 3 places
3.45 (2 decimal places)
× 2.8 (1 decimal place)
9.660 = 9.66 (3 places left)
÷
Division: Whole Divisor First
Rule 4
Make divisor a whole number: Move its decimal point all the way to the right.Shift dividend's decimal the same number of places.Float decimal point straight up into quotient.Divide normally using standard long division.
Example: \( 21.45 \div 1.5 \) Shift 1 Place
\( 1.5 \to 15 \) (moved 1 place right)
\( 126 \times 75 = 9450 \)
\( 36 \times 45 = 1620 \)
\( 1524 \times 305 = 464820 \)
Float decimal straight up:
Multiply by 10:
Multiply by 10:
Multiply by 100:
Multiply by 10:
Multiply by 100:
Number Fusion Answer Key • Topic 1: Decimals Page 1 of 3 Turn page for Topic 2: Mixed Numbers →
Teacher Scoring Key • Topic 2 Solutions
Mixed-Number Operations: Answer Key Grading Criteria: 0.5 pt LCD or improper conversion + 0.5 pt simplified final fraction Accept simplified mixed numbers or proper improper fractions
\( 2\frac{1}{4} + 3\frac{2}{4} \)
Like denom: \( (2+3) + \frac{1+2}{4} \)
Like denom. \( 5\frac{3}{4} \)
\( 4\frac{1}{3} + 2\frac{1}{6} \)
LCD = 6: \( 4\frac{2}{6} + 2\frac{1}{6} = 6\frac{3}{6} \)
Simplify \( 6\frac{1}{2} \)
\( 3\frac{3}{4} + 2\frac{5}{6} \)
LCD = 12: \( 3\frac{9}{12} + 2\frac{10}{12} = 5\frac{19}{12} \)
Improper sum \( 6\frac{7}{12} \)
\( 5\frac{2}{5} + 1\frac{7}{10} \)
LCD = 10: \( 5\frac{4}{10} + 1\frac{7}{10} = 6\frac{11}{10} \)
Rename \( 7\frac{1}{10} \)
\( 6\frac{5}{8} + 4\frac{3}{4} \)
LCD = 8: \( 6\frac{5}{8} + 4\frac{6}{8} = 10\frac{11}{8} \)
Eighths \( 11\frac{3}{8} \)
\( 7\frac{2}{3} + 5\frac{4}{5} \)
LCD = 15: \( 7\frac{10}{15} + 5\frac{12}{15} = 12\frac{22}{15} \)
Unlike 3, 5 \( 13\frac{7}{15} \)
\( 5\frac{5}{6} - 2\frac{1}{6} \)
\( 3\frac{4}{6} \) reduces to:
Reduce \( 3\frac{2}{3} \)
\( 6\frac{7}{8} - 3\frac{1}{4} \)
LCD = 8: \( 6\frac{7}{8} - 3\frac{2}{8} \)
No borrow \( 3\frac{5}{8} \)
\( 5\frac{1}{4} - 2\frac{3}{4} \)
Borrow 1: \( 4\frac{5}{4} - 2\frac{3}{4} = 2\frac{2}{4} \)
Regroup \( 2\frac{1}{2} \)
\( 7\frac{1}{3} - 4\frac{5}{8} \)
LCD = 24: \( 7\frac{8}{24} - 4\frac{15}{24} \)
LCD + borrow \( 2\frac{17}{24} \)
\( 8\frac{2}{5} - 3\frac{7}{10} \)
LCD = 10: \( 8\frac{4}{10} - 3\frac{7}{10} \)
Tenths borrow \( 4\frac{7}{10} \)
Rename 10 as \( 9\frac{7}{7} \):
From whole \( 5\frac{4}{7} \)
\( 1\frac{1}{2} \times 2\frac{2}{3} \)
\( \frac{3}{2} \times \frac{8}{3} = \frac{24}{6} \)
\( 2\frac{1}{4} \times 1\frac{1}{3} \)
\( \frac{9}{4} \times \frac{4}{3} = \frac{9}{3} \)
\( 2\frac{2}{5} \times 1\frac{7}{8} \)
\( \frac{12}{5} \times \frac{15}{8} = \frac{3 \times 3}{1 \times 2} \)
Or 4.5 \( 4\frac{1}{2} \)
\( 3\frac{1}{5} \times 2\frac{1}{2} \)
\( \frac{16}{5} \times \frac{5}{2} = \frac{16}{2} \)
\( 4\frac{2}{3} \times 1\frac{2}{7} \)
\( \frac{14}{3} \times \frac{9}{7} = \frac{2 \times 3}{1 \times 1} \)
\( 3\frac{3}{8} \times 2\frac{2}{9} \)
\( \frac{27}{8} \times \frac{20}{9} = \frac{3 \times 5}{2 \times 1} \)
Or 7.5 \( 7\frac{1}{2} \)
\( 3\frac{1}{2} \div 1\frac{3}{4} \)
\( \frac{7}{2} \div \frac{7}{4} = \frac{7}{2} \times \frac{4}{7} \)
\( 4\frac{2}{3} \div 1\frac{1}{6} \)
\( \frac{14}{3} \times \frac{6}{7} = \frac{2 \times 2}{1 \times 1} \)
\( 2\frac{5}{8} \div 1\frac{3}{4} \)
\( \frac{21}{8} \times \frac{4}{7} = \frac{3 \times 1}{2 \times 1} \)
Or 1.5 \( 1\frac{1}{2} \)
\( 5\frac{1}{3} \div 2\frac{2}{3} \)
\( \frac{16}{3} \times \frac{3}{8} = \frac{16}{8} \)
\( 3\frac{3}{5} \div 1\frac{1}{5} \)
\( \frac{18}{5} \div \frac{6}{5} = \frac{18}{6} \)
\( 6\frac{2}{5} \div 3\frac{1}{5} \)
\( \frac{32}{5} \times \frac{5}{16} = \frac{32}{16} \)
Number Fusion Answer Key • Topic 2: Mixed Numbers Page 2 of 3 Turn page for Topic 3: Mixed Representations →
Teacher Scoring Key • Topic 3 Solutions
Mixed Representations: Answer Key Page 3: 24 Pts Grand Total: 72 Pts
Dual Evaluation Policy: Either exact decimal or simplified fraction receives 100% credit Verify conversion fidelity between representations
Dec: \( 4.5 + 2.25 = 6.75 \)
Dec: \( 5.4 + 3.25 = 8.65 \)
\( 8\frac{13}{20} \) 8.65
\( 3\frac{3}{5} + 4.65 \)
Dec: \( 3.6 + 4.65 = 8.25 \)
\( 1.375 + 2\frac{1}{2} \)
Dec: \( 1.375 + 2.5 = 3.875 \)
\( 6\frac{7}{10} + 5.84 \)
Dec: \( 6.7 + 5.84 = 12.54 \)
\( 12\frac{27}{50} \) 12.54
\( 2\frac{3}{8} + 7.125 \)
Dec: \( 2.375 + 7.125 = 9.5 \)
Dec: \( 7.8 - 3.5 = 4.3 \)
\( 6\frac{1}{2} - 2.85 \)
Dec: \( 6.50 - 2.85 = 3.65 \)
\( 3\frac{13}{20} \) 3.65
\( 8.25 - 4\frac{3}{5} \)
Dec: \( 8.25 - 4.60 = 3.65 \)
\( 3\frac{13}{20} \) 3.65
\( 9\frac{3}{4} - 5.625 \)
Dec: \( 9.750 - 5.625 = 4.125 \)
\( 10.4 - 6\frac{4}{5} \)
Dec: \( 10.4 - 6.8 = 3.6 \)
\( 5\frac{1}{8} - 2.75 \)
Dec: \( 5.125 - 2.750 = 2.375 \)
\( 2\frac{1}{2} \times 0.6 \)
Dec: \( 2.5 \times 0.6 = 1.5 \)
\( 2\frac{4}{5} \times 1.5 \)
Dec: \( 2.8 \times 1.5 = 4.2 \)
\( 3.2 \times 1\frac{1}{4} \)
Dec: \( 3.2 \times 1.25 = 4.0 \)
\( 4\frac{1}{2} \times 0.8 \)
Dec: \( 4.5 \times 0.8 = 3.6 \)
\( 1\frac{3}{5} \times 2.25 \)
Dec: \( 1.6 \times 2.25 = 3.6 \)
\( 0.75 \times 3\frac{1}{3} \)
Frac: \( \frac{3}{4} \times \frac{10}{3} = \frac{10}{4} = 2\frac{1}{2} \)
\( 4.8 \div 1\frac{1}{5} \)
Dec: \( 4.8 \div 1.2 = 4 \)
\( 7.2 \div 1\frac{1}{5} \)
Dec: \( 7.2 \div 1.2 = 6 \)
\( 6\frac{1}{4} \div 2.5 \)
Dec: \( 6.25 \div 2.5 = 2.5 \)
\( 5.4 \div 2\frac{1}{4} \)
Dec: \( 5.4 \div 2.25 = 2.4 \)
\( 8\frac{2}{5} \div 1.4 \)
Dec: \( 8.4 \div 1.4 = 6 \)
\( 3\frac{3}{4} \div 0.5 \)
Dec: \( 3.75 \div 0.5 = 7.5 \)
Number Fusion Answer Key • Topic 3: Mixed Representations Page 3 of 3 Grand Total: 72 Problems Fully Keyed • Grade 7 Mastery
\( 21.45 \to 214.5 \) (moved 1 place right)
\( 214.5 \div 15 = \) 14.3
Must-Know Grade 7 Benchmark Equivalents Memorize these common fraction-decimal pairs
\( \frac{1}{4} \) | \( \frac{3}{4} \)
\( \frac{1}{5} \) | \( \frac{2}{5} \)
\( \frac{3}{5} \) | \( \frac{4}{5} \)
\( \frac{1}{8} \) | \( \frac{3}{8} \)
\( \frac{5}{8} \) | \( \frac{7}{8} \)
Watch Out (+ / -): Do NOT align digits by the right edge; always align by the decimal point!
Watch Out (×): Do NOT line up decimals when multiplying; count total decimal places at the very end.
Watch Out (Padding): In \( 10 - 2.45 \), write \( 10.00 \) first; never just "bring down" the 45.
Watch Out (÷): If divisor is already a whole number (e.g. \( 14.8 \div 4 \)), do not move the decimal!
Number Fusion Reference Sheet • Grade 7 Mathematics CCSS.MATH.CONTENT.7.NS.A.1, 7.NS.A.2, 7.EE.B.3 Keep in Study Folder
