Is 1/2 Bigger Than 4/5?

Q: Which is bigger: 1/2 or 4/5?

4/5 is bigger. As a decimal, 4/5 = 0.8 while 1/2 = 0.5.

Q: What is the difference between 1/2 and 4/5?

The difference is 3/10, which equals 0.3 in decimal form (30 percentage points).

Q: How do you compare 1/2 and 4/5?

You can use three methods: find a common denominator and compare numerators, cross-multiply and compare the products, or convert both fractions to decimals. All three methods confirm that 4/5 is greater than 1/2.

No, $\frac{1}{2}$ < $\frac{4}{5}$

$\frac{1}{2}$

50%

$\frac{4}{5}$

80%

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 2 and 5, and the least common denominator (LCD) is 10.

Step 1. Convert $\frac{1}{2}$: multiply numerator and denominator by 5. $\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$
Step 2. Convert $\frac{4}{5}$: multiply numerator and denominator by 2. $\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}$
Step 3. Compare the numerators: 5 vs 8.
Step 4. Since 5 is less than 8, we know that $\frac{1}{2} < \frac{4}{5}$.

Method 2: Cross Multiplication

A quicker way to compare fractions is to cross-multiply. Multiply each numerator by the other fraction's denominator:

Step 1. Multiply the numerator of the first fraction by the denominator of the second: $1 \times 5 = 5$.
Step 2. Multiply the numerator of the second fraction by the denominator of the first: $4 \times 2 = 8$.
Step 3. Compare the products: $5 < 8$, so $\frac{1}{2} < \frac{4}{5}$.

Method 3: Decimal Comparison

Convert each fraction to a decimal by dividing the numerator by the denominator:

$\frac{1}{2}$ as a decimal 0.5

$\frac{4}{5}$ as a decimal 0.8

Difference 0.3

Since 0.5 is less than 0.8, we confirm that $\frac{1}{2} < \frac{4}{5}$. In percentage terms, $\frac{1}{2}$ is 50% and $\frac{4}{5}$ is 80%, a difference of 30 percentage points.

Why Does This Work?

These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 10, we're cutting both quantities into equal-sized pieces. Then 5 pieces vs 8 pieces is a straightforward comparison.

Frequently Asked Questions

Which is bigger: 1/2 or 4/5?

$\frac{4}{5}$ is bigger. As a decimal, $\frac{4}{5}$ = 0.8 while $\frac{1}{2}$ = 0.5.

What is the difference between 1/2 and 4/5?

The difference is $\frac{3}{10}$, which equals 0.3 in decimal form (30 percentage points).

How do you compare 1/2 and 4/5?

You can use three methods: find a common denominator and compare numerators, cross-multiply and compare the products, or convert both fractions to decimals. All three methods confirm that $\frac{4}{5}$ $>$ $\frac{1}{2}$.

Keep Learning

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