Find the product of the following fractions. Express your answer in simplest form. 1. 3/11 x 4 5/6 = 2. 3 5/9 x 5/8= 3. 4 3/8 x 8/17 = 4. 12 2/5 x 5/6= 5. 5/10 x 3 2/6 = please help me with solution or step by step po..
The Correct Answer and Explanation is:
Let’s go through each one step by step.
1. 311×456\frac{3}{11} \times 4 \frac{5}{6}113×465
Step 1: Convert the mixed number to an improper fraction.
456=4×6+56=24+56=2964 \frac{5}{6} = \frac{4 \times 6 + 5}{6} = \frac{24 + 5}{6} = \frac{29}{6}465=64×6+5=624+5=629
Step 2: Multiply the fractions.
311×296=3×2911×6=8766\frac{3}{11} \times \frac{29}{6} = \frac{3 \times 29}{11 \times 6} = \frac{87}{66}113×629=11×63×29=6687
Step 3: Simplify the fraction.
We can divide both the numerator and denominator by 3:
87÷366÷3=2922\frac{87 \div 3}{66 \div 3} = \frac{29}{22}66÷387÷3=2229
So, the answer is 2922\frac{29}{22}2229.
2. 359×583 \frac{5}{9} \times \frac{5}{8}395×85
Step 1: Convert the mixed number to an improper fraction.
359=3×9+59=27+59=3293 \frac{5}{9} = \frac{3 \times 9 + 5}{9} = \frac{27 + 5}{9} = \frac{32}{9}395=93×9+5=927+5=932
Step 2: Multiply the fractions.
329×58=32×59×8=16072\frac{32}{9} \times \frac{5}{8} = \frac{32 \times 5}{9 \times 8} = \frac{160}{72}932×85=9×832×5=72160
Step 3: Simplify the fraction.
We can divide both the numerator and denominator by 8:
160÷872÷8=209\frac{160 \div 8}{72 \div 8} = \frac{20}{9}72÷8160÷8=920
So, the answer is 209\frac{20}{9}920.
3. 438×8174 \frac{3}{8} \times \frac{8}{17}483×178
Step 1: Convert the mixed number to an improper fraction.
438=4×8+38=32+38=3584 \frac{3}{8} = \frac{4 \times 8 + 3}{8} = \frac{32 + 3}{8} = \frac{35}{8}483=84×8+3=832+3=835
Step 2: Multiply the fractions.
358×817=35×88×17=280136\frac{35}{8} \times \frac{8}{17} = \frac{35 \times 8}{8 \times 17} = \frac{280}{136}835×178=8×1735×8=136280
Step 3: Simplify the fraction.
We can divide both the numerator and denominator by 8:
280÷8136÷8=3517\frac{280 \div 8}{136 \div 8} = \frac{35}{17}136÷8280÷8=1735
So, the answer is 3517\frac{35}{17}1735.
4. 1225×5612 \frac{2}{5} \times \frac{5}{6}1252×65
Step 1: Convert the mixed number to an improper fraction.
1225=12×5+25=60+25=62512 \frac{2}{5} = \frac{12 \times 5 + 2}{5} = \frac{60 + 2}{5} = \frac{62}{5}1252=512×5+2=560+2=562
Step 2: Multiply the fractions.
625×56=62×55×6=31030\frac{62}{5} \times \frac{5}{6} = \frac{62 \times 5}{5 \times 6} = \frac{310}{30}562×65=5×662×5=30310
Step 3: Simplify the fraction.
We can divide both the numerator and denominator by 10:
310÷1030÷10=313\frac{310 \div 10}{30 \div 10} = \frac{31}{3}30÷10310÷10=331
So, the answer is 313\frac{31}{3}331.
5. 510×326\frac{5}{10} \times 3 \frac{2}{6}105×362
Step 1: Convert the mixed number to an improper fraction.
326=3×6+26=18+26=2063 \frac{2}{6} = \frac{3 \times 6 + 2}{6} = \frac{18 + 2}{6} = \frac{20}{6}362=63×6+2=618+2=620
Step 2: Multiply the fractions.
510×206=5×2010×6=10060\frac{5}{10} \times \frac{20}{6} = \frac{5 \times 20}{10 \times 6} = \frac{100}{60}105×620=10×65×20=60100
Step 3: Simplify the fraction.
We can divide both the numerator and denominator by 20:
100÷2060÷20=53\frac{100 \div 20}{60 \div 20} = \frac{5}{3}60÷20100÷20=35
So, the answer is 53\frac{5}{3}35.
Summary of Answers:
- 2922\frac{29}{22}2229
- 209\frac{20}{9}920
- 3517\frac{35}{17}1735
- 313\frac{31}{3}331
- 53\frac{5}{3}35
By following these steps, you can multiply fractions and simplify your answers!
