8 divided by 3/5 ( in fraction or mixed number form
The Correct Answer and Explanation is:
Answer:8÷35=8×53=403=13138 \div \frac{3}{5} = 8 \times \frac{5}{3} = \frac{40}{3} = 13 \frac{1}{3}8÷53=8×35=340=1331
Explanation
To solve the expression 8 ÷ 3/5, we need to understand how division of fractions works.
Dividing by a fraction means multiplying by its reciprocal. The reciprocal of a fraction is simply the fraction flipped upside down. For example, the reciprocal of 35\frac{3}{5}53 is 53\frac{5}{3}35.
So, instead of dividing 8 by 35\frac{3}{5}53, we multiply 8 by the reciprocal of 35\frac{3}{5}53:8÷35=8×538 \div \frac{3}{5} = 8 \times \frac{5}{3}8÷53=8×35
Now, we convert 8 into a fraction to make the multiplication easier:8=818 = \frac{8}{1}8=18
Now we perform the multiplication:81×53=8×51×3=403\frac{8}{1} \times \frac{5}{3} = \frac{8 \times 5}{1 \times 3} = \frac{40}{3}18×35=1×38×5=340
So, 8÷35=4038 \div \frac{3}{5} = \frac{40}{3}8÷53=340. This is an improper fraction, meaning the numerator (top number) is greater than the denominator (bottom number). Improper fractions can also be expressed as mixed numbers.
To convert 403\frac{40}{3}340 into a mixed number, divide 40 by 3:
- 3 goes into 40 a total of 13 whole times (since 3 × 13 = 39),
- with a remainder of 1.
So, we write:403=1313\frac{40}{3} = 13 \frac{1}{3}340=1331
What does this mean? It means that if we divide 8 whole units into pieces that are 35\frac{3}{5}53 in size, we can make 13 full groups of 35\frac{3}{5}53, with 13\frac{1}{3}31 of a group left over.
This kind of division is important in real-life situations, such as recipes, sharing quantities, or measuring things accurately.
