Factor Power

2. Long Division: \(75 \div 5\) Quotient: 15

Steps: 5 into 7 tens is 1 (rem. 2). Bring down 5 to get 25.

5 into 25 ones is 5. Remainder = 0.

Fact link: Remind students that \(15 \times 5 = 75\), connecting multiplication to division.

3. Simplify: \(\frac{25}{60}\) Answer: \(\frac{5}{12}\)

GCF: 5 (Ends in 5 & 0 → common factor of 5).

Steps: \(\frac{25 \div 5}{60 \div 5} = \frac{5}{12}\).

Prompt: "Can 5 and 12 be simplified further? No, 5 is prime and does not divide 12."

4. Long Division: \(98 \div 7\) Quotient: 14

Steps: 7 into 9 tens is 1 (rem. 2). Bring down 8 to get 28.

7 into 28 ones is 4 (\(4 \times 7 = 28\)). Remainder = 0.

Check: \(10 \times 7 = 70\), \(4 \times 7 = 28\). \(70 + 28 = 98\).

Turn to Page 2 for Independent Practice Solutions & Decimal Breakdown Teacher Guide • Page 1 of 2

Part 3 & 4 Solutions Independent Mastery • Expert Problem Breakdown

Page 2 of 2

Independent Practice (You Do) Answer Key

5. \(\frac{45}{85}\) (Both end in 5)

GCF = 5

Work: \(\frac{45 \div 5}{85 \div 5} = \frac{9}{17}\)

\(\frac{9}{17}\)

6. \(91 \div 7\) (Divisor 7)

7 into 9 is 1 (rem. 2 tens)

Bring down 1 → 7 into 21 is 3

13

7. \(\frac{30}{80}\) (Both end in 0)

GCF = 10

Work: \(\frac{30 \div 10}{80 \div 10} = \frac{3}{8}\)

\(\frac{3}{8}\)

8. \(87 \div 3\) (Divisibility: \(8+7=15\))

3 into 8 is 2 (rem. 2 tens)

Bring down 7 → 3 into 27 is 9

29

9. \(\frac{35}{50}\) (Ends in 5 & 0)

GCF = 5

Work: \(\frac{35 \div 5}{50 \div 5} = \frac{7}{10}\)

\(\frac{7}{10}\)

10. \(\frac{18}{24}\) (Mixed Factors: 2, 3, 6)

GCF = 6

Work: \(\frac{18 \div 6}{24 \div 6} = \frac{3}{4}\)

\(\frac{3}{4}\)

Solution & Rubric

Expert Challenge: \(87.5 \div 5\)

Quotient: 17.5

Standard Algorithm Steps:

      1 7 . 5

    --------

  5 ) 8 7 . 5

    - 5        (5 × 1 ten = 5 tens)

    ---

      3 7      (3 tens + 7 ones = 37)

    - 3 5      (5 × 7 ones = 35)

    ---

        2 . 5  (2 ones = 20 tenths + 5 tenths = 25 tenths)

      - 2 . 5  (5 × 5 tenths = 2.5)

      -----

            0  (No remainder)

Place Value Key Understandings:

• Decimal Alignment: The decimal point in the quotient must be placed directly above the decimal point in 87.5 before dividing tenths.
• Divisibility by 5: Does it divide evenly? Yes [ X ]. Since the dividend ends in .5 (5 tenths), 5 divides 25 tenths with zero remainder.
• Fraction Equivalent: \(87.5 = 87\frac{1}{2} = \frac{175}{2}\). Dividing by 5 gives \(\frac{35}{2} = 17.5\).

Evaluation Note: Award 1 pt for decimal placement, 1 pt for accurate division algorithm, and 1 pt for correctly checking 'Yes' for zero remainder.

Tiered Differentiation Strategies

Support / Tier 2:

If students struggle to identify the GCF, have them list factor pairs on mini-whiteboards or use a 100-chart highlighter for multiples of 5 and 10. For long division, write D-M-S-B-R (Divide, Multiply, Subtract, Bring down, Repeat) on the board.

Extension / Challenge:

Challenge fast finishers to convert their simplest fractions into decimals using long division (e.g., divide \(3 \div 8\) from Problem 7 to prove \(\frac{3}{8} = 0.375\), or divide \(3 \div 4\) to show \(\frac{3}{4} = 0.75\)).

Factor Power • Grade 7 Standards Aligned Resource Teacher Guide • Page 2 of 2