Find the quotient in simplest form 1. 18:2 3/4 = 2. 30 = 2 5/6 = 3. 24/5-12 = 4. Divide four apples into halves. How many halves are there? 5. Cut your 12 meters into 1 2/3 meter. How many were you able to make? D. DIVISION OF MIXED FRACTION Rule: To divide mixed fractions, change mixed fraction to improper fraction. Multiply the dividend by the reciprocal of the divisor. Express answer to lowest term. Example: Mr. Cruz has 5 %2 hectares of land. He wants to give 1 3/8 hectare to each of his children, he will have no land left for himself. How many children does he have?
The Correct Answer and Explanation is:
Problem 1: 18234\frac{18}{2 \frac{3}{4}}24318
To solve this, let’s first convert the mixed fraction to an improper fraction.
- Convert 2342 \frac{3}{4}243 into an improper fraction:
234=2×4+34=8+34=1142 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}243=42×4+3=48+3=411
Now the problem becomes:18114=18×411\frac{18}{\frac{11}{4}} = 18 \times \frac{4}{11}41118=18×114
Multiply:18×411=7211\frac{18 \times 4}{11} = \frac{72}{11}1118×4=1172
Thus, the quotient in simplest form is 7211\frac{72}{11}1172.
Problem 2: 30÷25630 \div 2 \frac{5}{6}30÷265
Again, start by converting 2562 \frac{5}{6}265 into an improper fraction.
- Convert 2562 \frac{5}{6}265 into an improper fraction:
256=2×6+56=12+56=1762 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6}265=62×6+5=612+5=617
Now, we divide:30÷176=30×617=30×617=1801730 \div \frac{17}{6} = 30 \times \frac{6}{17} = \frac{30 \times 6}{17} = \frac{180}{17}30÷617=30×176=1730×6=17180
So, the quotient in simplest form is 18017\frac{180}{17}17180.
Problem 3: 245−12\frac{24}{5} – 12524−12
First, we convert 12 into a fraction with the same denominator as 245\frac{24}{5}524.12=12×55=60512 = \frac{12 \times 5}{5} = \frac{60}{5}12=512×5=560
Now subtract:245−605=24−605=−365\frac{24}{5} – \frac{60}{5} = \frac{24 – 60}{5} = \frac{-36}{5}524−560=524−60=5−36
So, the result is −365\frac{-36}{5}5−36.
Problem 4: Divide four apples into halves. How many halves are there?
Each apple can be divided into 2 halves. Since there are 4 apples, we multiply:4×2=84 \times 2 = 84×2=8
So, there are 8 halves.
Problem 5: Cut 12 meters into 1231 \frac{2}{3}132 meter pieces. How many pieces can be made?
Convert 1231 \frac{2}{3}132 into an improper fraction:123=1×3+23=3+23=531 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}132=31×3+2=33+2=35
Now, divide 12 meters by 53\frac{5}{3}35:12÷53=12×35=12×35=36512 \div \frac{5}{3} = 12 \times \frac{3}{5} = \frac{12 \times 3}{5} = \frac{36}{5}12÷35=12×53=512×3=536
Now, simplify:365=715\frac{36}{5} = 7 \frac{1}{5}536=751
So, you can make 7 full pieces and one extra piece that is 15\frac{1}{5}51 of a meter.
Example Problem: How many children does Mr. Cruz have?
Mr. Cruz has 5125 \frac{1}{2}521 hectares of land, and he wants to give 1381 \frac{3}{8}183 hectares to each child. We need to find how many children can receive this amount of land.
First, convert both mixed numbers into improper fractions.
- Convert 5125 \frac{1}{2}521 to an improper fraction:
512=5×2+12=10+12=1125 \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2}521=25×2+1=210+1=211
- Convert 1381 \frac{3}{8}183 to an improper fraction:
138=1×8+38=8+38=1181 \frac{3}{8} = \frac{1 \times 8 + 3}{8} = \frac{8 + 3}{8} = \frac{11}{8}183=81×8+3=88+3=811
Now, divide 112\frac{11}{2}211 by 118\frac{11}{8}811:112÷118=112×811\frac{11}{2} \div \frac{11}{8} = \frac{11}{2} \times \frac{8}{11}211÷811=211×118
Simplify:11×82×11=8822=4\frac{11 \times 8}{2 \times 11} = \frac{88}{22} = 42×1111×8=2288=4
Thus, Mr. Cruz has 4 children.
Conclusion
- The quotient of 18234\frac{18}{2 \frac{3}{4}}24318 is 7211\frac{72}{11}1172.
- The quotient of 30÷25630 \div 2 \frac{5}{6}30÷265 is 18017\frac{180}{17}17180.
- The result of 245−12\frac{24}{5} – 12524−12 is −365\frac{-36}{5}5−36.
- There are 8 halves in 4 apples.
- You can cut 12 meters into 7 full 1231 \frac{2}{3}132 meter pieces with one extra 15\frac{1}{5}51 of a meter piece.
- Mr. Cruz has 4 children.
