# Basic Operations with Fractions and Mixed Numbers

Quick Review: Fractions, Mixed Numbers and Averages

g. Find the average of the scores: 45, 55, 80, 35, 65
h. Two-fifths of the students in a school have school lunch. There are 890 students altogether.
How many students do not have school lunch?

Group Work / Homework Assignment: Fractions and Mixed Numbers
1. Evaluate the following. Write answer in lowest terms .

2. Find the average of

3. There are two bags of rice. One bag weighs kg and the other weighs kg. If
of the total weight is sold, find the weight of the remaining rice.

4. Ex press as a single fraction in lowest terms:

5. Simplify:

6. Simplify:

7. There are 252 marbles in a bag. If two-sevenths of them are red, four-ninths of the remainder
are green, and the rest are blue, how many blue marbles are there?
8. A piece of string was m long. A boy cut off m of the string and gave it to his sister.
He then cut off two-thirds of the remaining length for his cousin. What was the length of the
remaining piece of string?

Part II - Basic Operations with Decimals

Quick Review

a. 3.21 x 2.3
b. 36.5
÷ 5
c. 57.5
÷ 0.23
d. 33.8 + 9.35
e. 62.123 - 4.24

Group Work / Homework Assignment

1. 0.7 x 0.6 x 0.05
2. 28.5 + 12.35 + 48.2
3. 16.3 - 2.087
4. 5.8 + 6.2 x 0.2
5. 173.88
÷ 0.63
6. 5 x (2 + 0.2)
÷ 4 16

7. Sue’s mother bought 5 lemons at \$0.25 each, ½ kg of meat at \$8.36 per kg, and 2.5 L of milk
at \$0.85 per ½ L. How much money did she spend altogether?

Part III - Conversions between Fractions and Decimals

Quick Review
1. Fractions may be thought of as division problems . To convert a fraction to a decimal, divide
the denominator into the numerator. Divide until the answer terminates or until the repeating
pattern is apparent and put a bar over the repeating part.

2. Some times it is easier to write an equivalent fraction with a denominator that is a power of 10,
such as 10, 100, 1000, etc. (This may always be done if the prime factors of the denominator are
only 2's or 5's or both.)

(Note: multiply numerator and denominator by the missing factors in order to get only
factors of 10 in the denominator.)

3. To convert a decimal to a fraction : Say the decimal in words, write the fraction, reduce.

0.012 Say , and reduce to

Group Work / Homework Assignment

1. Convert into fractions to lowest terms: a. 0.425 b. 0.0024 c. 3.2 d. 0.00005
2. Convert to decimal form:
3. Simplify the following . Give your answer either in fraction or decimal form.

Part IV - Percentage

Quick Review
1. Convert to fraction: 26%
2. Convert to percent:

3. Convert to fraction:
4. Convert to decimal:
5. Find 30% of \$450.

6. There are 2,310 children in a school. This number is 5% more than it was last year. Calculate
the number of children in the school last year.

Group Work / Homework
1. Express 45% as: a. a decimal b. a reduced fraction

2. Express as a percent:

3. Express as: a. a decimal b. a reduced fraction

4. A merchant received his order of 250 ceramic figurines and found that 8% of them were
broken. How many figurines were unbroken?

5. There are 1,500 soccer players in a county league. 45% of them are boys.
a.. What percent of the players are girls?
b. How many boys are there in the league?

6. In 1983, the population of a town was 72,000. In 1993, the population had risen to 81,000.
Find the percent increase of the population.

7. The enrollment of a certain elementary school was 450 in 1999. By 2000, the enrollment had
increased by 16%. What was the enrollment in 2000?

8. What is of 800 m?
9. Express 50 minutes as a percentage of 3 hours.
10. The price of a jacket is increased by 25% to \$95, what was the original price?
11. If the price of a hat is decreased by 5% to \$19, what was the original price?

Applied problems from New Elementary Mathematics Syllabus D, by Sin Kwai Meng, with
Editor Dr. Wong Khoon Yoong, (2006), have been utilized in this workshop.

Part I
Quick review

g. 56 h.534 students

Group work/HW
Fractions and Mixed Numbers

Part II
Quick Review
a. 7.383
b. 7.3
c. 250
d. 43.15
d. 57.883

Group work/HW
1. 0.021
2. 89.05
3. 14.213
4. 7.04
5. 276
6.
7. \$9.68

Part III
Quick Review

Group work/HW

Part IV
Quick Review

1.13/50
2 a. 25% b. 140% c. 35%
3 a.13/20 b.1/8
4 a. 0.34 b. 0.0025
5. \$135
6. 2200 children

Group work/HW

1 a. 0.45 b.9/20
2 a. 100% b. 80% c. 0.03% d. 15% e. 235% f. 115%
3 a. 0.086 b.43/100
4. 230 figurines
5 a. 55% girls b. 675 boys
6. 12.5%
7. 522
8. 42m
9.
10. \$76
11. \$20

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