unit #1 basic mathematics (2017)
example 10. divide 5/18 by 5/9, which means 5/18 ÷ 5/9. no lcd is needed.
5/18 ÷ 5/9 = 5/18 · 9/5 = 1/2 invert the second fraction and multiply. 9/5 is called the reciprocal of 5/9.
calculator. enter 5 a/b 18 ÷ 5 a/b 9 =. displays 1 _ 2 or 1/2.
answer. the quotient is 1/2.
exercise 7. operations with fractions
perform the appropriate operation(s) and simplify using a calculator.
1. find the sum of 4/5 and 7/8.
2. find the sum of 5 5/8 and 9 3/4.
3. find the difference of 3 11/12 minus 1 2/3.
4. subtract 45 5/12 from 61. (hint. the “from” number comes first.)
5. find the product. 5/8 × 2/3 =
6. find the product of 2 1/2 and 3 5/8.
7. find the quotient. 3 3/4 ÷ 1 2/3 =
8. divide 5 by 5/12.
9. find 7/8 × 2/3 ÷ 1/8. (reminder. pemdas)
10. calculate. 3/5 ÷ (1/2 · 3/10) (hint. enter parentheses in any calculator.)
11. 1/4 + 1/2 · 2/3 =
12. 5/8 - 1/2 + 4(1/6) =
fractional part of a whole
example 11. sam and marie ran for president of the math club. sam got 15 votes, and marie got the other 10 votes. what fraction of the total votes did sam receive?
solution. fraction = part/whole = sams votes/total votes = 15/(10 + 15) = 15/25 = 3/5 reduce.
answer. sam got 3/5 of the total votes.

Question

Accepted Answer

1.
# Explanation:
## Step1: Find common - denominator
The common denominator of 5 and 8 is 40.
$\frac{4}{5}+\frac{7}{8}=\frac{4	imes8}{5	imes8}+\frac{7	imes5}{8	imes5}=\frac{32}{40}+\frac{35}{40}$
## Step2: Add numerators
$\frac{32 + 35}{40}=\frac{67}{40}=1\frac{27}{40}$
# Answer:
$1\frac{27}{40}$

2.
# Explanation:
## Step1: Convert mixed - numbers to improper fractions
$5\frac{5}{8}=\frac{5	imes8 + 5}{8}=\frac{45}{8}$ and $9\frac{3}{4}=\frac{9	imes4+3}{4}=\frac{39}{4}$
The common denominator of 8 and 4 is 8.
$\frac{45}{8}+\frac{39}{4}=\frac{45}{8}+\frac{39	imes2}{4	imes2}=\frac{45}{8}+\frac{78}{8}$
## Step2: Add numerators
$\frac{45 + 78}{8}=\frac{123}{8}=15\frac{3}{8}$
# Answer:
$15\frac{3}{8}$

3.
# Explanation:
## Step1: Convert mixed - numbers to improper fractions
$3\frac{11}{12}=\frac{3	imes12 + 11}{12}=\frac{47}{12}$ and $1\frac{2}{3}=\frac{1	imes3+2}{3}=\frac{5}{3}$
The common denominator of 12 and 3 is 12.
$\frac{47}{12}-\frac{5}{3}=\frac{47}{12}-\frac{5	imes4}{3	imes4}=\frac{47}{12}-\frac{20}{12}$
## Step2: Subtract numerators
$\frac{47-20}{12}=\frac{27}{12}=2\frac{3}{12}=2\frac{1}{4}$
# Answer:
$2\frac{1}{4}$

4.
# Explanation:
## Step1: Convert mixed - number to improper fraction
$45\frac{5}{12}=\frac{45	imes12 + 5}{12}=\frac{545}{12}$ and $61=\frac{61	imes12}{12}=\frac{732}{12}$
## Step2: Subtract numerators
$\frac{732}{12}-\frac{545}{12}=\frac{732 - 545}{12}=\frac{187}{12}=15\frac{7}{12}$
# Answer:
$15\frac{7}{12}$

5.
# Explanation:
## Step1: Multiply numerators and denominators
$\frac{5}{8}	imes\frac{2}{3}=\frac{5	imes2}{8	imes3}=\frac{10}{24}$
## Step2: Simplify fraction
$\frac{10\div2}{24\div2}=\frac{5}{12}$
# Answer:
$\frac{5}{12}$

6.
# Explanation:
## Step1: Convert mixed - numbers to improper fractions
$2\frac{1}{2}=\frac{2	imes2 + 1}{2}=\frac{5}{2}$ and $3\frac{5}{8}=\frac{3	imes8+5}{8}=\frac{29}{8}$
## Step2: Multiply numerators and denominators
$\frac{5}{2}	imes\frac{29}{8}=\frac{5	imes29}{2	imes8}=\frac{145}{16}=9\frac{1}{16}$
# Answer:
$9\frac{1}{16}$

7.
# Explanation:
## Step1: Convert mixed - numbers to improper fractions
$3\frac{3}{4}=\frac{3	imes4 + 3}{4}=\frac{15}{4}$ and $1\frac{2}{3}=\frac{1	imes3+2}{3}=\frac{5}{3}$
## Step2: Invert and multiply
$\frac{15}{4}\div\frac{5}{3}=\frac{15}{4}	imes\frac{3}{5}=\frac{15	imes3}{4	imes5}=\frac{45}{20}$
## Step3: Simplify fraction
$\frac{45\div5}{20\div5}=\frac{9}{4}=2\frac{1}{4}$
# Answer:
$2\frac{1}{4}$

8.
# Explanation:
## Step1: Write 5 as a fraction
$5=\frac{5}{1}$
## Step2: Invert and multiply
$\frac{5}{1}\div\frac{5}{12}=\frac{5}{1}	imes\frac{12}{5}=\frac{5	imes12}{1	imes5}=12$
# Answer:
$12$

9.
# Explanation:
## Step1: Multiply first two fractions
$\frac{7}{8}	imes\frac{2}{3}=\frac{7	imes2}{8	imes3}=\frac{14}{24}=\frac{7}{12}$
## Step2: Divide by the third fraction
$\frac{7}{12}\div\frac{1}{8}=\frac{7}{12}	imes\frac{8}{1}=\frac{7	imes8}{12	imes1}=\frac{56}{12}=\frac{14}{3}=4\frac{2}{3}$
# Answer:
$4\frac{2}{3}$

10.
# Explanation:
## Step1: Calculate inside the parentheses
$\frac{1}{2}	imes\frac{3}{10}=\frac{1	imes3}{2	imes10}=\frac{3}{20}$
## Step2: Divide
$\frac{3}{5}\div\frac{3}{20}=\frac{3}{5}	imes\frac{20}{3}=\frac{3	imes20}{5	imes3}=4$
# Answer:
$4$

11.
# Explanation:
## Step1: Multiply first
$\frac{1}{2}	imes\frac{2}{3}=\frac{1	imes2}{2	imes3}=\frac{1}{3}$
## Step2: Add
$\frac{1}{4}+\frac{1}{3}=\frac{1	imes3}{4	imes3}+\frac{1	imes4}{3	imes4}=\frac{3}{12}+\frac{4}{12}=\frac{3 + 4}{12}=\frac{7}{12}$
# Answer:
$\frac{7}{12}$

12.
# Explanation:
## Step1: Calculate the multiplication
$4	imes\frac{1}{6}=\frac{4}{6}=\frac{2}{3}$
## Step2: Find common - denominator for addition and subtraction
The common denominator of 8, 2, and 3 is 24.
$\frac{5}{8}-\frac{1}{2}+\frac{2}{3}=\frac{5	imes3}{8	imes3}-\frac{1	imes12}{2	imes12}+\frac{2	imes8}{3	imes8}=\frac{15}{24}-\frac{12}{24}+\frac{16}{24}$
## Step3: Perform addition and subtraction
$\frac{15-12 + 16}{24}=\frac{19}{24}$
# Answer:
$\frac{19}{24}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find common - denominator

Step2: Add numerators

Step1: Convert mixed - numbers to improper fractions

Step2: Add numerators

Step1: Convert mixed - numbers to improper fractions

Step2: Subtract numerators

Answer: