### Fraction Lengths

Can you find combinations of strips of paper which equal the length of the black strip? If the length of the black is 1, how could you write the sum of the strips?

Can you find ways to make twenty-link chains from these smaller chains?

# Fractional Wall

##### Stage: 2 Challenge Level:

Thanks to the many of you who submitted a solution to this problem. Congratulations to Josie, Dominic and George from St Nicholas CE Junior School, Newbury and also Abigail from Histon Junior School and Charlie from Beckley C of E who all sent in clearly explained solutions. The solution given below was sent in by Cong:

Using the image above, I can find $\frac{1}{2}$ as:
$1$ blue ($\frac{1}{2}$)
$2$ dark greens ($\frac{2}{4}$)
$3$ pinks ($\frac{3}{6}$)
$4$ light greens ($\frac{4}{8}$)
$6$ reds ($\frac{6}{12}$)
$12$ whites ($\frac{12}{24}$)

So I can also say that $$\frac{1}{2}= \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{6}{12} = \frac{12}{24}$$

From the picture, I can find $\frac{1}{3}$ as:
$1$ brown ($\frac{1}{3}$)
$2$ pinks ($\frac{2}{6}$)
$4$ reds ($\frac{4}{12}$)
$8$ whites ($\frac{8}{24}$)

So I can also say that $$\frac{1}{3} = \frac{2}{6} = \frac{4}{12} = \frac{8}{24}$$

Again, using the image of the fraction wall, I can find $\frac{3}{4}$ as:
$3$ dark greens ($\frac{3}{4}$)
$6$ light greens ($\frac{6}{8}$)
$9$ reds ($\frac{9}{12}$)
$18$ whites ($\frac{18}{24}$)

So again I can say that $$\frac{3}{4}= \frac{6}{8} = \frac{9}{12} = \frac{18}{24}$$

The rule for working out equivalent fractions is to multiply the numerator and the denominator with the same whole number.