Question

find the product. check whether your answer is reasonable.

1. estimate: 3,500

51×74

1. estimate: 1,000

30×28

1. estimate: 2,000

40×35

1. estimate: 4,800

82×63

1. estimate: 3,600

36×93

1. estimate: 1,200

57×22

1. dig deeper! find the missing digits. then find the product.

□5×□6
1 0 0
5 0
6 0
+ 3 0
□□0

1. modeling real life if newton meets his goal each month, how many liters of water will he drink in 1 year?

monthly water intake goals
you ★★★★★★★★
newton ★★★★★
descartes ★
each ★ = 6 liters.

1. modeling real life use the table in exercise 11. if you and descartes each meet your goal each month, how many more liters will you drink in 1 year than descartes?
2. review & refresh

add or subtract. then check your answer.

1. 512,006+318,071=
2. 746,620 - 529,706=

Explanation:

Step1: Solve problem 10

We know that \(5\times6 = 30\). Let the first - number be \(a5\) and the second number be \(b6\). The product of the units - digits is \(5\times6=30\). The product \(a5\times b6=(10a + 5)\times(10b+6)=100ab+60a + 50b+30\). Since \(5\times b\) gives a number ending with 0, \(b = 2\). And \(a\times6\) gives a number ending with 0, \(a = 1\). So \(15\times26=390\).

Step2: Solve problem 11

Newton has 5 stars for his monthly water - intake goal. Each star represents 6 liters. So his monthly water intake is \(5\times6 = 30\) liters. In 1 year (12 months), he will drink \(30\times12=360\) liters.

Step3: Solve problem 12

You have 7 stars and Descartes has 1 star for their monthly water - intake goals. The difference in the number of stars per month is \(7 - 1=6\) stars. Each star represents 6 liters, so the monthly difference is \(6\times6 = 36\) liters. In 1 year (12 months), the difference is \(36\times12 = 432\) liters.

Step4: Solve problem 13

\[

$$\begin{align*} 512006+318071&=(500000 + 12000+6)+(300000+18000 + 71)\\ &=(500000+300000)+(12000 + 18000)+(6 + 71)\\ &=800000+30000+77\\ &=830077 \end{align*}$$

\]

Step5: Solve problem 14

\[

$$\begin{align*} 746620-529706&=746620-(529000+706)\\ &=746620 - 529000-706\\ &=217620-706\\ &=216914 \end{align*}$$

\]

Answer:

1. The missing digits are 1 and 2, and the product is 390.
2. 360 liters
3. 432 liters
4. 830077
5. 216914