Question
Write down all your working to show that the following statement is correct.
\(\frac{1+\frac{8}{9}}{2+\frac{1}{2}}=\frac{34}{45}\)
▶️Answer/Explanation
We can add the fractions in the numerator:
\(1+\frac{8}{9}=\frac{9+8}{9}=\frac{17}{9}\)
We can convert the mixed number to an improper fraction ,
\(2+\frac{1}{2}=\frac{4+1}{2}=\frac{5}{2}\)
Now, we can substitute the simplified numerator and denominator back into the original expression:
\(\Rightarrow \frac{\frac{17}{9}}{\frac{5}{2}}=\frac{17}{9}\times \frac{2}{5}=\frac{17\times 2}{9\times 5}\)
\(=\frac{34}{45}\)
Question
(a) Write 326.413 correct to 2 significant figures.
(b) Find the square root of one million.
(c) Calculate
\(\frac{64.3+7.465}{5.2-3.65}.\)
▶️Answer/Explanation
(a) To write 326.413 correct to 2 significant figures, we need to consider the first two non-zero digits from the left.
326.413 has the first two non-zero digits as 3 and 2.
Therefore, 326.413 correct to 2 significant figures is 330.
(b)The square root of one million can be found by taking the square root of 10^6, which is equal to 1000.
Therefore, the square root of one million is 1000 or \(10^{3}.\)
(c)\(\Rightarrow \frac{64.3+7.465}{5.2-3.65}=\frac{71.765}{1.55}=46.3\)
Question
Without using your calculator, work out \(1\frac{5}{6}+\frac{9}{10}.\)
You must show your working and give your answer as a mixed number in its simplest form.
▶️Answer/Explanation
\(=1\frac{5}{6}+\frac{9}{10}\)
\(=\frac{6\times 1+5}{6}+\frac{9}{10}\)
\(=\frac{11}{6}+\frac{9}{10}\)
\(=\frac{11\times 10+9\times 6}{60}\)
\(=\frac{110+54}{60}\)
\(=\frac{164}{60}\)
\(=2\frac{11}{15}\)
Question
Give each answer as a fraction in its lowest terms.
Work out.
(a) \(\frac{3}{4} – \frac{1}{12}\)
(b) \(2 \frac{1}{2} \times \frac{4}{25}\).
▶️Answer/Explanation
(a)\(\frac{3}{4}-\frac{1}{12}\)
The least common multiple (LCM) of 4 and 12 is 12. Therefore, we will convert the fractions to have a denominator of 12.
\(=\frac{3\times 3-1}{12}\)
\(=\frac{8}{12}\)
\(=\frac{2}{3}\)
Thus,\(\frac{3}{4}-\frac{1}{12} \)in simplest form is\( \frac{2}{3}.\)
(b)\(2\frac{1}{2}\times \frac{4}{25}\)
\(=\frac{2\times 2+1}{2}\times \frac{4}{25}\)
\(=\frac{5}{2}\times \frac{4}{25}\)
\(=\frac{20}{50}\)
\(=\frac{2}{5}\)
Thus, \(2\frac{1}{2}\times \frac{4}{25} \)is \(\frac{2}{5}\) in its simplest form.
Question
Show that \(1 \frac{1}{2} \div \frac{3}{16} = 8\).
Do not use a calculator and show all the steps of your working.
▶️Answer/Explanation
Convert the mixed number to an improper fraction
\(1\frac{1}{2}\) can be written as \(\frac{3}{2}\).
Take reciprocal of second fraction
To divide by a fraction, we multiply by its reciprocal. The reciprocal of \(\frac{3}{16}\) is \(\frac{16}{3}.\)
Multiply the fractions
Now, we multiply the two fractions
\(\frac{3}{2}\times \frac{16}{3}\)
\(\frac{3\times 16}{2\times 3}=\frac{48}{6}=8\)
Therefore, \(1\frac{1}{2}\div \frac{3}{16}=8\)