# How do you write 7 ¼ as an improper fraction?

Mar 16, 2018

See an explanation below:

#### Explanation:

$7 \frac{1}{4} = 7 + \frac{1}{4} = \left(\frac{4}{4} \times 7\right) + \frac{1}{4} = \frac{28}{4} + \frac{1}{4} = \left(28 + 1\right) 4 = \frac{29}{4}$

The quick rule is:

• Multiply the integer by the denominator: $7 \times 4 = 28$

• Add the numerator to this product: $28 + 1 = 29$

• Put this result over the denominator: $\frac{29}{4}$

$I \frac{n}{d} = \frac{\left(I \times d\right) + n}{d}$

$7 \frac{1}{4} = \frac{\left(7 \times 4\right) + 1}{4} = \frac{28 + 1}{4} = \frac{29}{4}$

Mar 16, 2018

$7 \frac{1}{4} = \frac{4 \times 7 + 1}{4} = \frac{29}{4}$

#### Explanation:

When a number is given an improper fraction, it means the entire number is given as a number of portions.

If the portion size is quarters, the improper fraction will show how many quarters there are altogether.
Note than every whole number is $\frac{4}{4}$

If the portion size is thirds, the improper fraction will show how many thirds there are altogether.
Note than every whole number is $\frac{3}{3}$

If the portion size is sixths, the improper fraction will show how many sixths there are altogether.
Note than every whole number is $\frac{6}{6}$

In this case we have $7 \frac{1}{4}$ which is made up of $7$ whole numbers and an extra $\frac{1}{4}$

In each of the $7$ whole numbers there are $\frac{4}{4}$....

Altogether that is $7 \times 4 = 28$ quarters, written as $\frac{28}{4}$

But there is an extra $\frac{1}{4}$, meaning we have $\frac{29}{4}$

To calculate it quickly:

$7 \frac{1}{4} = \frac{4 \times 7 + 1}{4} = \frac{29}{4}$