Solve Mixed Number Division: 2⅐ ÷ ¼ Step-by-Step

Question

+217:+14= ? +2\frac{1}{7}:+\frac{1}{4}=\text{ ?}

Video Solution

Solution Steps

00:00 Solve
00:06 Positive divided by positive is always positive
00:19 Convert mixed fraction to fraction
00:53 Let's substitute this fraction in our exercise
01:05 Division is also multiplication by the reciprocal
01:15 Switch between numerator and denominator
01:25 Make sure to multiply numerator by numerator and denominator by denominator
01:39 Break down 60 into 56 plus 4
01:47 Break down the fraction into whole number and remainder
01:52 Convert whole fraction to whole number
02:02 And this is the solution to the question

Step-by-Step Solution

Let's first convert 2 and seven-sevenths into a simple fraction:

217=2+17=2×77+17=2×77+17=147+17=14+17=157 2\frac{1}{7}=2+\frac{1}{7}=2\times\frac{7}{7}+\frac{1}{7}=\frac{2\times7}{7}+\frac{1}{7}=\frac{14}{7}+\frac{1}{7}=\frac{14+1}{7}=\frac{15}{7}

Now the exercise we have is:

157:14= \frac{15}{7}:\frac{1}{4}=

next we convert the division exercise into a multiplication exercise, remembering to switch the numerator and denominator in the second fraction:

157×41= \frac{15}{7}\times\frac{4}{1}=

Let's now combine into one multiplication exercise:

15×47×1=607 \frac{15\times4}{7\times1}=\frac{60}{7}

Next, we factor 60 into an addition exercise:

56+47= \frac{56+4}{7}=

Then let's separate the exercise into addition between fractions:

567+47= \frac{56}{7}+\frac{4}{7}=

Finally, we solve the first fraction exercise to get our answer:

8+47=847 8+\frac{4}{7}=8\frac{4}{7}

Answer

847 8\frac{4}{7}