Question

adding and subtracting fractions with different denominator

1. raul walked 12 6/7 km on monday. he walked 8 2/3 more on friday. how many more km did he walk on monday than on friday?
2. emily measured her mum and dad. her mum was 1 2/3 metres tall and her dad was 1 6/8 metres tall. how much taller is her dad than her mum?
3. juno bought two books. the first book weighed 1 2/5 kg. the second book weighed 1 5/6 kg. how much do the books weigh in total?

challenge
use the following pairs of fractions and write your own addition and subtract
remember to work out the answer to your own questions!

1. 2 1/3 + 1 6/11

Explanation:

Question 6

Step1: Identify the distances

Raul walked \( 12\frac{6}{7} \) km on Monday and \( 8\frac{2}{3} \) km on Friday. We need to find the difference \( 12\frac{6}{7}-8\frac{2}{3} \).

Step2: Convert to improper fractions

\( 12\frac{6}{7}=\frac{12\times7 + 6}{7}=\frac{90}{7} \)
\( 8\frac{2}{3}=\frac{8\times3+2}{3}=\frac{26}{3} \)

Step3: Find a common denominator

The least common multiple of 7 and 3 is 21.
\( \frac{90}{7}=\frac{90\times3}{7\times3}=\frac{270}{21} \)
\( \frac{26}{3}=\frac{26\times7}{3\times7}=\frac{182}{21} \)

Step4: Subtract the fractions

\( \frac{270}{21}-\frac{182}{21}=\frac{270 - 182}{21}=\frac{88}{21} \)

Step5: Convert back to mixed number

\( \frac{88}{21}=4\frac{4}{21} \)

Step1: Identify the heights

Mum's height: \( 1\frac{2}{3} \) m, Dad's height: \( 1\frac{6}{8} \) m (simplify \( 1\frac{6}{8}=1\frac{3}{4} \)). We need \( 1\frac{3}{4}-1\frac{2}{3} \).

Step2: Convert to improper fractions

\( 1\frac{3}{4}=\frac{1\times4 + 3}{4}=\frac{7}{4} \)
\( 1\frac{2}{3}=\frac{1\times3+2}{3}=\frac{5}{3} \)

Step3: Find a common denominator

LCM of 4 and 3 is 12.
\( \frac{7}{4}=\frac{7\times3}{4\times3}=\frac{21}{12} \)
\( \frac{5}{3}=\frac{5\times4}{3\times4}=\frac{20}{12} \)

Step4: Subtract the fractions

\( \frac{21}{12}-\frac{20}{12}=\frac{1}{12} \)

Step1: Identify the weights

First book: \( 1\frac{2}{5} \) kg, Second book: \( 1\frac{5}{6} \) kg. We need \( 1\frac{2}{5}+1\frac{5}{6} \).

Step2: Convert to improper fractions

\( 1\frac{2}{5}=\frac{1\times5 + 2}{5}=\frac{7}{5} \)
\( 1\frac{5}{6}=\frac{1\times6+5}{6}=\frac{11}{6} \)

Step3: Find a common denominator

LCM of 5 and 6 is 30.
\( \frac{7}{5}=\frac{7\times6}{5\times6}=\frac{42}{30} \)
\( \frac{11}{6}=\frac{11\times5}{6\times5}=\frac{55}{30} \)

Step4: Add the fractions

\( \frac{42}{30}+\frac{55}{30}=\frac{42 + 55}{30}=\frac{97}{30} \)

Step5: Convert back to mixed number

\( \frac{97}{30}=3\frac{7}{30} \)

Answer:

\( 4\frac{4}{21} \) km

Question 7