**High School Number Sense Lesson 30: Estimating the Multiplication of Fractions**

This type of problem has come and go over the years, but it had a strong showing this year. It appeared

**10 times**on high school tests, usually at

**question # 30**.

**Number Dojo Level: 174**

Estimation problems, like I've said before, are the most commonly missed problems on number sense tests. I have noticed that these particular questions seem to be skipped more often than they are attempted. With a little bit of attention, they can be solved without much effort.

Typically (especially this year), you will be asked to multiply a mixed number by a whole number and then divide by a different whole number. When you convert the mixed number to an improper fraction, you can usually get rid of common factors with the fraction. It sounds complicated, but I will break it down for you with a few examples from this year's tests:

**Example 1: * 2 1/4 x 92015 ÷ 9**

- Convert the mixed number to an improper fraction. 2 1/4 =
**9/4**. You now have**9/4 x 92015 ÷ 9.** - Rearrange the order, and you have
**9/4 ÷ 9 x 92015**. Notice that the 9's cancel out. You are left with**1/4 x 92015**, which is the same as**92015 ÷ 4**. - Rounding, we get
**92000 ÷ 4**. The answer is**23000**. - The exact answer is
**23003.75**, so the acceptable (+/- 5%) range would be**21854 - 24153**. We are well within range.

**Example 2: * 3 1/5 x 12515 ÷ 16**

- Convert the mixed number to an improper fraction. 3 1/5 =
**16/5**. You now have**16/5 x 12515 ÷ 16**. - Rearrange the order, and you have
**16/5 ÷ 16 x 12515**. Notice that the 16's cancel out. You are left with**1/5 x 12515**, which is the same as**12515 ÷ 5**. - Rounding, we get
**12500 ÷ 5**. The answer is**2500**. - The exact answer is
**2503**, so the acceptable (+/- 5%) range would be**2378 - 2628**. We are well within range.

**Example 3: * 4 2/7 x 6390 ÷ 15**

- Convert the mixed number to an improper fraction. 4 2/7 =
**30/7**. You now have**30/7 x 6390 ÷ 15**. - Rearrange the order, and you have
**30/7 ÷ 15 x 6390**. Notice that the 15's cancel out. You are left with**2/7 x 6390**, which is the same as**6390 ÷ 7 x 2**. - Rounding, we get
**6300 ÷ 7 x 2**, which is**900 x 2**, which is**1800**. - The exact answer is
**1825 5/7**, so the acceptable (+/- 5%) range would be**1735 - 1917**. We are safely within range.

**Example 4: * 9 3/5 ÷ 96 x 36550**

- Convert the mixed number to an improper fraction. 9 3/5 = 48/5. You now have
**48/5 ÷ 96 x 36550**. - Notice that the 48's cancel out. You are left with
**1/5 ÷ 2 x 36550**. - 1/5 ÷ 2 =
**1/10**. You are left with**1/10 x 36550**. We don't even have to round; the answer is**3655**. - The acceptable (+/- 5%) range would be
**3473 - 3837**. We are (obviously) within range.

__: you may have noticed that 9 3/5 is the same as 9.6, so you could've changed the problem to__

**Note****9.6**

**÷ 96 x 36550**. This may have saved a little time.

**Example 5: * 33 23/70 x 17900**

- This one looks a little different; it showed up as question # 80 on a middle school test. The idea here is that
**33 23/70**is painfully close to**33 23/69**, which is the same as**33 1/3**. 33 1/3, as discussed previously, is exactly**1/3 of 100**or**100/3**. - The problem becomes
**100/3 x 17900**, which can be rearranged as**17900 ÷ 3 x 100**. - Rounding, we get
**18000 ÷ 3 x 100**, which is**6000 x 100**, which is**600000**. - The exact answer is
**596581 3/7**, so the acceptable (+/- 5%) range would be**566753 - 626410**. We are safely within range.

**Here's a free worksheet to help you practice EstMultFrac:**

estmultfrac.pdf |

**Up Next for High School: MultEnd5**