Test Yourself Fractions
Here's a really quick way of testing if you've learned the methods
used in this section. Look at the sum on the card and see if you
can work out its answer.
If you get stuck, press method to help you remember.
To check if you're right, press the card.
Go through the whole list to see how many sums you can answer.
Revisit any that you had difficulty remembering, until you're confident you can
solve all of them.
47+25
3435
$\frac{4}{7}+\frac{2}{5}$47+25
If adding or subtracting is your aim the bottom numbers must be the same.
Multiply the top and bottom of each fraction by the other fraction's denominator:
$\frac{4}{7}\times\frac{5}{5}=\frac{20}{35}$47×55=2035
$\frac{2}{5}\times\frac{7}{7}=\frac{14}{35}$25×77=1435
$\left(\frac{1}{2}+\frac{1}{2}=\frac{1+1}{2}\right)$(12+12=1+12) so,
$\frac{20}{35}+\frac{14}{35}=\frac{20+14}{35}=\frac{34}{35}$2035+1435=20+1435=3435
Answer: $\frac{4}{7}+\frac{2}{5}=\frac{34}{35}$47+25=3435
23-19
59
$\frac{2}{3}-\frac{1}{9}$23−19
If adding or subtracting is your aim the bottom numbers must be the same.
Multiply the top and bottom of each fraction by the other fraction's denominator:
$\frac{2}{3}\times\frac{9}{9}=\frac{18}{27}$23×99=1827
$\frac{1}{9}\times\frac{3}{3}=\frac{3}{27}$19×33=327
$\left(\frac{1}{2}-\frac{1}{2}=\frac{1-1}{2}\right)$(12−12=1−12) so,
$\frac{18}{27}-\frac{3}{27}=\frac{18-3}{27}=\frac{15}{27}$1827−327=18−327=1527
Now simplify the fraction:
$\frac{15\div3}{27\div3}=\frac{5}{9}$15÷327÷3=59
Answer: $\frac{2}{3}-\frac{1}{9}=\frac{5}{9}$23−19=59
212×37
1114
$2\frac{1}{2}\times\frac{3}{7}$212×37
Change $2\frac{1}{2}$212 to a fraction (an improper fraction).
$2\frac{1}{2}=2+\frac{1}{2}=\frac{2}{1}+\frac{1}{2}$212=2+12=21+12
If adding or subtracting is your aim the bottom numbers must be the same.
Multiply the top and bottom of each fraction by the other fraction's denominator:
$\frac{2}{1}\times\frac{2}{2}=\frac{4}{2}$21×22=42
$\frac{1}{2}\times\frac{1}{1}=\frac{1}{2}$12×11=12
$\left(\frac{1}{2}+\frac{1}{2}=\frac{1+1}{2}\right)$(12+12=1+12) so,
$\frac{4}{2}+\frac{1}{2}=\frac{4+1}{2}=\frac{5}{2}$42+12=4+12=52
We can now multiply:
$\frac{5}{2}\times\frac{3}{7}$52×37
( $\frac{1}{2}\times\frac{1}{2}$12×12 or $\frac{1}{2}$12 of a $\frac{1}{2}=\frac{1\times1}{2\times2}=\frac{1}{4}$12=1×12×2=14 ) so,
$\frac{5}{2}\times\frac{3}{7}=\frac{5\times3}{2\times7}=\frac{15}{14}$52×37=5×32×7=1514
Now simplify the fraction:
$1\frac{1}{14}$1114
Answer: $2\frac{1}{2}\times\frac{3}{7}=1\frac{1}{14}$212×37=1114
43÷23
2
$\frac{4}{3}\div\frac{2}{3}$43÷23
When dividing fractions think 'Kentucky Chicken Fried'.
K = keep C = change the sign F = flip the last fraction
$\frac{4}{3}\times\frac{3}{2}$43×32
($\frac{1}{2}\times\frac{1}{2}$12×12 or $\frac{1}{2}$12 of a $\frac{1}{2}=\frac{1\times1}{2\times2}=\frac{1}{4}$12=1×12×2=14) so,
$\frac{4}{3}\times\frac{3}{2}=\frac{12}{6}=2$43×32=126=2
Answer: $\frac{4}{3}\div\frac{2}{3}=2$43÷23=2
