Number Morph Guided Notes
Math Lab • Pre-Algebra Unit 3: Rational Numbers
Number Morph Guided Notes
Mastering conversions between Fractions, Decimals, and Percents
NAME:
DATE:
PERIOD:
1
The Conversion Triangle (Anchor Visual)
Follow the arrows to morph any number!
FRACTION
Part over whole: \( \frac{\text{numerator}}{\text{denominator}} \)
\(\frac{1}{2}\) \(\frac{3}{4}\) \(\frac{4}{5}\)
Fraction ➔ Decimal Divide top by bottom (\( \text{num} \div \text{den} \))
Decimal ➔ Percent Multiply by 100 (Shift 2 spots ➡️)
DECIMAL
Place values: tenths, hundredths
PERCENT
Per hundred: \( \text{value}\% \)
2
Pathway A: Fraction ⇄ Decimal
FRACTION ➔ DECIMAL Method: Long Division
Rule: Divide the numerator by the denominator. Top goes inside the "house"!
Worked Example:
Convert \( \frac{3}{8} \) to decimal: \( 3 \div 8 = 0.375 \)
✏️ Your Turn (Show Work):
1. Convert \( \frac{4}{5} \):
2. Convert \( \frac{5}{6} \):
DECIMAL ➔ FRACTION Method: Place Value
Rule: Read the decimal by place value, write it over 10, 100, or 1000, and simplify!
Worked Example:
Convert \( 0.64 \): \( \frac{64}{100} \div \frac{4}{4} = \frac{16}{25} \)
✏️ Your Turn (Write & Simplify):
1. Convert \( 0.35 \):
2. Convert \( 0.08 \):
3
Pathway B: Decimal ⇄ Percent (The Two-Step Slide)
DECIMAL ➔ PERCENT Slide RIGHT ➡️ 2x
Rule: Multiply by \( 100 \) (move the decimal point 2 places right) and attach the \( \% \) symbol.
Worked Example:
\( 0.425 \times 100 = \) \( 42.5\% \)
✏️ Your Turn:
1. \( 0.7 = \)
2. \( 0.045 = \)
PERCENT ➔ DECIMAL Slide LEFT ⬅️ 2x
Rule: Divide by \( 100 \) (move decimal point 2 places left) and remove the \( \% \) symbol.
Worked Example:
\( 85\% \div 100 = \) \( 0.85 \)
✏️ Your Turn:
1. \( 6\% = \)
2. \( 135\% = \)
Number Morph Guided Notes • Page 1 of 2 Remember: "Percent" literally means "out of 100"
Page 2
Direct Conversions & Benchmark Mastery
Name:
4
Pathway C: Fraction ⇄ Percent
FRACTION ➔ PERCENT (Scale Denominator)
When the denominator is a factor of 100 (e.g. \( 2, 4, 5, 10, 20, 25, 50 \)), multiply to make the bottom 100!
Worked Example:
\( \frac{7}{20} \times \frac{5}{5} = \frac{35}{100} = \) \( 35\% \)
✏️ Your Turn:
1. Convert \( \frac{9}{25} \):
2. Convert \( \frac{13}{50} \):
PERCENT ➔ FRACTION (Simplify)
Place the number over 100, remove the \( \% \) sign, then simplify by dividing by the Greatest Common Factor.
Worked Example:
\( 72\% = \frac{72}{100} \div \frac{4}{4} = \) \( \frac{18}{25} \)
✏️ Your Turn:
1. Convert \( 45\% \):
2. Convert \( 28\% \):
5
The Benchmark Hall of Fame
Fill in the missing values to memorize these keys!
| FRACTION | DECIMAL | PERCENT | VISUAL BENCHMARK |
|---|
| \( \frac{1}{2} \) | \( 0.5 \) | \( 50\% \) | |
| | | |
| \( \frac{1}{4} \) | \( 0.25 \) | | |
|
|
| \( \frac{3}{4} \) |
| \( 75\% \) |
|
| \( \frac{1}{5} \) | \( 0.2 \) |
|
|
|
| \( 0.1 \) | \( 10\% \) |
|
| \( \frac{1}{3} \) | \( 0.\overline{3} \) |
|
|
6
Master The Trio (Fill the Missing Forms)
Challenge 1
Fraction: \( \frac{3}{5} \)
Decimal:
Percent:
Challenge 2
Fraction:
Decimal: \( 0.15 \)
Percent:
Challenge 3
Fraction:
Decimal:
Percent: \( 48\% \)
!
Common Pitfall Alert: Watch The Zeroes!
Remember that \( 5\% = 0.05 \), NOT \( 0.5 \) (which is \( 50\% \)). When sliding decimals two spaces, always fill empty spots with a placeholder zero (e.g. \( 0.08 \rightarrow 8\% \), and \( 7\% \rightarrow 0.07 \)).
Number Morph Guided Notes • Page 2 of 2 Check your work: Use a calculator to divide fraction numerators and denominators!
