Question

I am studying for my mid terms them this question popped up;
What are the sums of the following pairs of numbers?
a) 45 and 67 b) 2366 and 734 c) 399 and 60987 d) 908.34 and 456.88
I just got so confused! Can someone please give me the answers or at least help me? I'm begging! (I'm only in 7th grade btw) :p

Answer 1

Answer on Question#38548 - Math- Algebra

Question: What are the sums of the following pairs of numbers?

a) 45 and 67

b) 2366 and 734

c) 399 and 60987

d) 908.34 and 456.88

Solution.

a) 45 and 67

Let us separate the addends into units and tens:

$$\begin{array}{l} 45 = 40 + 5 \\ 67 = 60 + 7 \\ \end{array}$$

and add the units first:

$$5 + 7 = 12.$$

Now add the tens:

$$40 + 60 = 100.$$

After that, we need to add the two numbers from previous steps:

$$100 + 12 = 112.$$

We can also use column addition:

$$\begin{array}{c} 4\ 5 \\ + \quad 6\ 7 \\ \hline 1\ 1\ 2 \\ \end{array}$$

b) 2366 and 734

Similarly to the previous problem, separate the addends into units, tens, hundreds and thousands:

$$2366 = 2000 + 300 + 60 + 6$$ $$734 = 700 + 30 + 4$$

and add the units first:

$$6 + 4 = 10.$$

Then, add the tens:

$$60 + 30 = 90,$$

and hundreds:

$$300 + 700 = 1000.$$

Note that 734 is less than 1000, so for thousands we have

$$2000 + 0 = 2000.$$

Now, let us add the sums of units, tens, hundreds and thousands:

$$2000 + 1000 + 90 + 10 = 3000 + 100 = 3100.$$

Or, using column addition,

$$\begin{array}{c} 2\ 3\ 6\ 6 \\ + \quad 7\ 3\ 4 \\ \hline 3\ 1\ 0\ 0 \\ \end{array}$$

c) 399 and 60987

Note that according to the commutative law of addition, $399 + 60987 = 60987 + 399$.

As before, separate the addends into units, tens, hundreds, thousands and tens of thousands:

$$60987 = 60000 + 900 + 80 + 7$$ $$399 = 300 + 90 + 9$$

and add the units:

$$7 + 9 = 16,$$

tens:

$$80 + 90 = 170,$$

and hundreds:

$$900 + 300 = 1200.$$

For thousands and tens of thousands, we have

$$60000 + 0 = 60000.$$

Now add the numbers from previous steps:

$$60000 + 1200 + 170 + 16 = 60000 + 1200 + 186 = 60000 + 1386 = 61386,$$

or

$$+ \frac{60987}{61386}$$

d) 908.34 and 456.88

These numbers are not integers; we can add the fractional part first (in the same manner as we did for integers). To do this, we need to repeat the already familiar procedure:

$$908.34 = 900 + 8 + 0.3 + 0.04$$ $$456.88 = 400 + 50 + 6 + 0.8 + 0.08$$

Now, add the fractional part:

$$0.04 + 0.08 = 0.12$$

and

$$0.3 + 0.8 = 1.1.$$

Next, add the units:

$$8 + 6 = 14,$$

tens:

$$0 + 50 = 50$$

and hundreds:

$$900 + 400 = 1300.$$

Finally, add these sums together:

$$1300 + 50 + 14 + 1.1 + 0.12 = 1300 + 50 + 14 + 1.22 = 1300 + 50 + 15.22 = 1300 + 65.22 = 1365.22.$$

Or, using column addition:

$$+ \frac{908.34}{1365.22}$$

Answer.

a) 112

b) 3100

c) 61386

d) 1365.22