Fractions with Denominators of 10 and 100

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Concept Review

The Great Fraction Makeover: From 10ths to 100ths

Imagine you have a chocolate bar divided into 10 equal pieces, and you eat 3 pieces. Now imagine your friend has the exact same amount of chocolate, but their bar is divided into 100 tiny squares. How many squares did your friend eat? This is the magic of equivalent fractions!

When we have a fraction with 10 in the denominator (bottom number), we can always transform it into an equivalent fraction with 100 in the denominator. It's like zooming in with a magnifying glass — we're looking at the same amount, just in smaller, more detailed pieces.

The "Times 10" Transform

Here's the secret: to change any fraction with denominator 10 into denominator 100, we multiply both the top and bottom by 10. Why does this work? Because 10 × 10 = 100!

Step-by-Step Example

Let's transform 3/10 into hundredths:

3/10 = ?/100

↓

(3 × 10)/(10 × 10) = 30/100

So 3/10 = 30/100. Three-tenths equals thirty-hundredths!

Think about money to see why this makes sense. 3 dimes equals 30 pennies. A dime is 1/10 of a dollar, and a penny is 1/100 of a dollar. When we have 3 dimes, we have 3/10 of a dollar, which is exactly the same as 30 pennies or 30/100 of a dollar.

🔑 Key Insight

Every fraction with denominator 10 has a "twin" with denominator 100. The numerator (top number) always becomes 10 times bigger, but the fraction's value stays exactly the same. It's like trading 1 ten-dollar bill for 10 one-dollar bills — different pieces, same total value!

More Quick Transforms

7/10

↓ ×10/×10

70/100

1/10

↓ ×10/×10

10/100

🎯 Key Takeaway

Just like that chocolate bar from our opening question, 3/10 and 30/100 represent the exact same amount — we're just describing it with different-sized pieces. Mastering this transformation gives you the power to work flexibly with fractions and prepares you for decimals, where this skill becomes essential!

Sample questions

1. How do you turn 3/10 into an equivalent fraction with a denominator of 100?

○ Add a zero to only the denominator (3/100)

○ Add 90 to the denominator

✓ Multiply both numerator and denominator by 10 (30/100)

○ It is already equivalent

Answer: Multiply both numerator and denominator by 10 (30/100) — To keep the fraction balanced, you must scale the numerator by the same factor of 10.

2. If you have 7/10 of a dollar, how many pennies (hundredths) is that?

✓ 70/100

○ 7/100

○ 700/100

○ 10/70

Answer: 70/100 — 7 dimes = 70 pennies. $7/10 = 70/100$.

3. Which fraction is equivalent to 5/10?

○ 5/100

✓ 50/100

○ 10/50

○ 1/10

Answer: 50/100 — 5/10 is half, and 50/100 is also half.

Skills in this topic

Express a fraction with denominator 10 as an equivalent fraction with denominator 100
Add two fractions with respective denominators 10 and 100
Find missing numerators to make an equation with tenths and hundredths true
Use visual base-ten blocks to represent tenths and hundredths
Convert fractional amounts of money (e.g., 30/100 of a dollar)

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