How many 5/16s are in 1 whole 7/8?
The correct answer and explanation is:
To find how many 516\frac{5}{16} are in 1781 \frac{7}{8}, we follow these steps:
Step 1: Convert the mixed number into an improper fraction
178=8×1+78=1581 \frac{7}{8} = \frac{8 \times 1 + 7}{8} = \frac{15}{8}
Step 2: Divide the total amount (158\frac{15}{8}) by the part size (516\frac{5}{16})
When you divide by a fraction, you multiply by its reciprocal: 158÷516=158×165\frac{15}{8} \div \frac{5}{16} = \frac{15}{8} \times \frac{16}{5}
Step 3: Multiply the fractions
Multiply the numerators and denominators: 15×168×5=24040=6\frac{15 \times 16}{8 \times 5} = \frac{240}{40} = 6
✅ Final Answer: 6
Explanation (300 words):
This question asks how many parts of size 516\frac{5}{16} fit into a larger value of 1781 \frac{7}{8}. To solve this, we begin by converting the mixed number 1781 \frac{7}{8} into an improper fraction, which is easier to work with in division. We convert it to 158\frac{15}{8} by multiplying the whole number part (1) by the denominator (8) and adding the numerator (7), giving us 8+78=158\frac{8 + 7}{8} = \frac{15}{8}.
Next, to find out how many of 516\frac{5}{16} fit into 158\frac{15}{8}, we divide the two fractions. Dividing fractions involves multiplying the first fraction by the reciprocal of the second. The reciprocal of 516\frac{5}{16} is 165\frac{16}{5}, so we multiply 158×165\frac{15}{8} \times \frac{16}{5}.
When we multiply across, 15×16=24015 \times 16 = 240 and 8×5=408 \times 5 = 40, which gives 24040\frac{240}{40}. Simplifying this gives 6.
This means that you can fit exactly six pieces of 516\frac{5}{16} into 1781 \frac{7}{8}. This concept is important in real-life applications, such as measuring ingredients, dividing materials, or working with medication dosages where a total amount is split into equal parts. Understanding how to divide fractions helps in all these contexts.