For Problems 1 and 2, determine the missing values.
a. [latex] \displaystyle{\frac{9}{15} = \frac{?}{10} = \frac{15}{?}} [/latex]
b. [latex] \displaystyle{\frac{18}{27} = \frac{?}{18} = \frac{10}{?}} [/latex]
c. [latex] \displaystyle{\frac{21}{35} = \frac{?}{25} = \frac{12}{?}} [/latex]
d. [latex] \displaystyle{\frac{12}{28} = \frac{?}{70} = \frac{15}{?}} [/latex]
a. [latex] \displaystyle{\frac{6}{12} = \frac{?}{6} = \frac{24}{?}} [/latex]
b. [latex] \displaystyle{\frac{12}{45} = \frac{?}{15} = \frac{16}{?}} [/latex]
c. [latex] \displaystyle{\frac{20}{25} = \frac{?}{5} = \frac{12}{?}} [/latex]
d. [latex] \displaystyle{\frac{36}{48} = \frac{?}{36} = \frac{18}{?}} [/latex]
For Problems 3 and 4, place the appropriate symbol (<, >, or =) between each of the fractions.
a. [latex] \displaystyle{\frac{15}{18}} [/latex] ▢ [latex] \displaystyle{\frac{30}{42}} [/latex]
b. [latex] \displaystyle{\frac{21}{24}} [/latex] ▢ [latex] \displaystyle{\frac{35}{40}} [/latex]
c. [latex] \displaystyle{\frac{40}{48}} [/latex] ▢ [latex] \displaystyle{\frac{35}{42}} [/latex]
d. [latex] \displaystyle{\frac{8}{38}} [/latex] ▢ [latex] \displaystyle{\frac{12}{57}} [/latex]
a. [latex] \displaystyle{\frac{24}{21}} [/latex] ▢ [latex] \displaystyle{\frac{11}{5}} [/latex]
b. [latex] \displaystyle{\frac{20}{44}} [/latex] ▢ [latex] \displaystyle{\frac{6}{15}} [/latex]
c. [latex] \displaystyle{\frac{18}{45}} [/latex] ▢ [latex] \displaystyle{\frac{16}{4}} [/latex]
d. [latex] \displaystyle{\frac{15}{25}} [/latex] ▢ [latex] \displaystyle{\frac{63}{100}} [/latex]
For Problems 5 and 6, convert the improper fractions into mixed numbers in simplest form.
a. [latex] \displaystyle{\frac{18}{8}} [/latex]
b. [latex] \displaystyle{\frac{98}{12}} [/latex]
c. [latex] \displaystyle{\frac{88}{10}} [/latex]
d. [latex] \displaystyle{\frac{48}{15}} [/latex]
a. [latex] \displaystyle{\frac{15}{10}} [/latex]
b. [latex] \displaystyle{\frac{39}{26}} [/latex]
c. [latex] \displaystyle{\frac{88}{12}} [/latex]
d. [latex] \displaystyle{\frac{102}{9}} [/latex]
For Problems 7 and 8, reduce the fractions to their lowest terms.
a. [latex] \displaystyle{\frac{36}{144}} [/latex]
b. [latex] \displaystyle{\frac{68}{10}} [/latex]
c. [latex] \displaystyle{\frac{80}{12}} [/latex]
d. [latex] \displaystyle{\frac{61}{366}} [/latex]
a. [latex] \displaystyle{\frac{75}{345}} [/latex]
b. [latex] \displaystyle{\frac{124}{48}} [/latex]
c. [latex] \displaystyle{\frac{70}{14}} [/latex]
d. [latex] \displaystyle{\frac{292}{365}} [/latex]
For Problems 9 to 12, express the decimal numbers in their word form.
a. 0.75
b. 0.3
c. 0.008
d. 0.04
a. 0.5
b. 0.007
c. 0.12
d. 0.029
a. 27.602
b. 470.5
c. 32,010.07
d. 3,500,007.45
a. 32.04
b. 200.2
c. 45,005.001
d. 1,005,071.25
For Problems 13 and 14, perform the indicated arithmetic operations.
a. 716.03 + 49.936
b. 15.71 − 3.509
c. 15.71 × 3.26
d. 39.83 ÷ 9
a. 478.82 + 85.847
b. 65.09 − 24.987
c. 54.37 × 1.46
d. 77.09 ÷ 8
What is the sum of the least and the greatest numbers of the following?
0.041, 0.011, 0.014, 0.01
What is the difference between the least and the greatest numbers of the following?
0.012, 0.201, 0.02, 0.102
Which of the following is closest to 2?
2.011, 2.004, 1.997, 1.996
Which of the following is closest to 2?
2.011, 2.005, 1.996, 1.995
For Problems 19 and 20, convert the decimal numbers to proper fractions in lowest terms and the fractions to decimal numbers.
| Table | Decimal Number | Proper Fraction |
|---|---|---|
| a. | 0.06 | ? |
| b. | ? | [latex] \displaystyle{\frac{23}{50}} [/latex] |
| c. | 0.075 | ? |
| d. | ? | [latex] \displaystyle{\frac{27}{40}} [/latex] |
| e. | 0.004 | ? |
| f. | ? | [latex] \displaystyle{\frac{17}{25}} [/latex] |
| Table | Decimal Number | Proper Fraction |
|---|---|---|
| a. | 0.025 | ? |
| b. | ? | [latex] \displaystyle{\frac{5}{8}} [/latex] |
| c. | 0.08 | ? |
| d. | ? | [latex] \displaystyle{\frac{7}{25}} [/latex] |
| e. | 0.002 | ? |
| f. | ? | [latex] \displaystyle{\frac{39}{50}} [/latex] |
Alex used [latex] \displaystyle{2\frac{1}{5}} [/latex] litres of paint for his bedroom, [latex] \displaystyle{1\frac{1}{4}} [/latex] litres for his study room, and [latex] \displaystyle{7\frac{1}{3}} [/latex] litres for his living room. How many litres of paint did he use for the three rooms?
Find the total weight of three items that weigh [latex] \displaystyle{3\frac{2}{3}} [/latex] kg, [latex] \displaystyle{4\frac{1}{2}} [/latex] kg, and [latex] \displaystyle{5\frac{3}{8}} [/latex] kg.
Harsha purchased [latex] \displaystyle{12\frac{1}{3}} [/latex] hectares of land and sold [latex] \displaystyle{4\frac{2}{5}} [/latex] hectares. How many hectares does she now own?
Henry is [latex] \displaystyle{8\frac{1}{4}} [/latex] years old. Amanda is [latex] \displaystyle{2\frac{5}{12}} [/latex] years old. How many years younger is Amanda than Henry?
Samantha can walk [latex] \displaystyle{5\frac{3}{8}} [/latex] km in one hour. How far can she walk in [latex] \displaystyle{4\frac{1}{3}} [/latex] hours?
A car can travel [latex] \displaystyle{8\frac{1}{4}} [/latex] km with one litre of gas. How many kilometres can it travel using [latex] \displaystyle{45\frac{3}{5}} [/latex] litres of gas?
Andy and Bob had $128. One-third of Bob’s amount is $25. How much did each of them have?
Alisha and Beyonce saved a total of $580. Two-fifths of Alisha’s savings equals $144. How much did each of them save?
George’s car had 12.47 litres of gas at the start of his trip to the United States. He added the following quantities of gas during his trip: 34.25 litres, 15.2 litres, and 20.05 litres. At the end of the trip, there were 7.9 litres of gas left in the car. How much gas was used during the trip?
Lakshmi had $2,675.68 in her chequing account. She deposited 2 cheques in the amounts of $729.27 and $72.05 and withdrew $1,275.60. How much did she have in her account after the withdrawal?
Carol’s overtime rate of pay is $57.45 per hour. If Carol worked 12.5 hours overtime last week, calculate her gross overtime pay for last week.
Barbie’s hourly pay is $23.07. If Barbie worked 37.75 hours last week, calculate her gross pay for last week.
There are 3,400 spectators at a soccer match. Threefifths of the number of men equals six-sevenths of the number of women. How many spectators are women?
Three-fourths of the number of boys at a school is equal to half of the number of girls. The school has 480 students in total. How many more girls are there than boys?
For Problems 35 to 46, evaluate the expressions.
[latex] \displaystyle{\left(\frac{5}{7}\right)^2 \div 5 + \sqrt{3^2 + 4^2}} [/latex]
[latex] \displaystyle{\left(5+ \frac{6}{10}\right)^3 + \sqrt{6^2 + 8^2}} [/latex]
[latex] \displaystyle{\sqrt{0.81} - (0.2)^2 + \sqrt{\frac{9}{36}}} [/latex]
[latex] \displaystyle{\sqrt{1.21} - (0.5)^2 + \sqrt{\frac{4}{25}}} [/latex]
[latex] \displaystyle{\left(\frac{2}{3}\right)^3 + \left(\frac{2}{9}\right)^2} [/latex]
[latex] \displaystyle{\left(\frac{1}{5}\right)^3 + \left(\frac{4}{25}\right)^2} [/latex]
[latex] \displaystyle{\left(\frac{4}{7}\right)^2\left(\frac{1}{4}\right)^3} [/latex]
[latex] \displaystyle{\left(\frac{5}{12}\right)^3\left(\frac{4}{5}\right)^2} [/latex]
[latex] \displaystyle{\left(2\frac{5}{8} + 1\frac{5}{12}\right) \div 1\frac{1}{2}} [/latex]
[latex] \displaystyle{\left(2\frac{4}{5} - \frac{7}{10}\right) \div 2\frac{4}{52}} [/latex]
[latex] \displaystyle{2\frac{2}{3} \div \left(2\frac{2}{5} + 6)} [/latex]
[latex] \displaystyle{3\frac{1}{5} \div \left(1\frac{1}{5} + 1)} [/latex]