Answer to Question #246674 in Algebra for elisa

Question

Question 1 Explain the terms (a) numerator, (b) denominator.

Question 2 Express 24/40 and 18/42 in their simplest forms.

Question 3 a) Express the fractions 2/3, 3/4 and 5/6 as equivalent fractions with a denominator of 12.

b) A library contains 60,000 books. 14,000 are on the subject of business, 22,000 are on healthcare and 12,000 on psychology and law. What percentage of the library’s books is on computing, if computing books make up two-thirds of the remainder?

Question 4 A sports shop in Manchester is doing a sale on some merchandise. Liz hears about it and goes to make a purchase of two pairs of running shoes. She gives the sales attendant in the store three crisp £50 notes and is given change of £10.50. What is the price of each pair of running shoes? Show your working.

Question 5 a) What is 240.50 x 19.54? Give your answer to 2 significant figures.

b) Write the number 52100 as a power of 10. 

Answer 1

1

a

When numbers are written in the form of a fraction, it can be represented as ^a⁄_b

The top part (a) is called the numerator.

b

When numbers are written in the form of a fraction, it can be represented as ^a⁄_b

The bottom part (b) is called the denominator.

2

a

Find the GCD (or HCF) of numerator and denominator

GCD of 24 and 40 is 8

Divide both the numerator and denominator by the GCD

$\frac{24 ÷ 8 }{ 40 ÷ 8}$

The simplest form of $\frac{24} {40}$ is $\frac{3}{5}$

b

Find the GCD (or HCF) of numerator and denominator

GCD of 18 and 42 is 6

Divide both the numerator and denominator by the GCD

$\frac{24 ÷ 6 }{ 42 ÷ 6}$

The simplest form of $\frac{18} {42}$ is $\frac{3}{7}$

3.

a

Given the following fractions

2/3, 3/4 and 5/6

We are to write as equivalent fractions with a denominator of

12​

For the fraction 2/3;

$=\frac{2\times 4}{3\times4}=\frac{8}{12}$

For the fraction 3/4

$=\frac{3\times 3}{4\times3}=\frac{9}{12}$

For the fraction 5/6;

$=\frac{5\times 2}{6\times2}=\frac{10}{12}$

b

Remaining books $=60000-(14000+22000+12000)=12000$

computing books $=\frac{2}{3}\times12000=8000$

percentage$=\frac{8000}{60000}\times 100=13.33\%$

4

$50-10.5=39.50$

$=39.50\div 2$

$= 19.75$

5.

$a.\\ 240.50 \times 19.54=4699.37$

b.

$52100 \\=5.21\times 10^4$