$3467+2859$

Break it into place values:

$=(3000+2000)+(400+800)+(60+50)+(7+9)$

$=5000+1200+110+16$

$=(5000+1000)+(200+100)+(10+10)+6$

$=6000+300+20+6$

$=6326$

$7532-4268$

Break it down:

$=(7000-4000)+(500-200)+(30-60)+(2-8)$

We can use negative numbers.

$=3000+300-30-6$

$=3000+270-6$

$=3000+264$

$=3264$

Try It: Solve $6743+3185$ and $8301-4527$

$2374+1648$

Start with 2375

• Add 1000
• Add 600
• Add 40
• Add 8

$2375+1000=3375$

$3375+600=3975$

$3975+40=4015$

$4015+8=4023$

$=4023$

$5623-2487$

Start with 5623

• Subtract 2000
• Subtract 400
• Subtract 80
• Subtract 7

$5628-2000=3623$

$3623-400=3223$

$3223-80=3143$

$3143-7=3136$

$=3136$

Try It: Solve $7235+4528$ and $9801-5643$

$4998+3276$

Instead of adding directly, round 4998 to 5000 (adding 2) and adjust at the end:

$5000+3276=8276$

Now subtract the extra 2. (The inverse operation of adding 2 from above):

$8276-2=8274$

$=8274$

$8012-4991$

Instead of subtracting directly, round 4991 up to 5000 (a difference of 9) and adjust at the end. (Note: Why did we adjust the second number, but not the first?)

$8012-5000=3012$

Now add back the extra 9 (Going from 5000 back to 4991):

$3012+9=3021$

$=3021$

Try It: Solve $7999+3482$ and $9004-4998$

$6315-2478=3837$

Check by adding:

$3837+2478=6315$✓

$4329+5672=10.001$

Check by subtracting:

$\mathrm{10,001}-5672=4329$✓

Try It: Solve $8675-3492$ and check with addition.

$4\times 3$

Multiplication represents repeated addition. So 4 × 3 means adding 3 four times.

$=3+3+3+3$

$=12$

You invest $1000 in a savings account that earns 5% simple interest per year. How much money will you have after 4 years using repeated addition?

Interest for 1 year:

Interest

$=1000\times 0.05=50$

After 1 year:

$\$1000+50=\$1050$

Use repeated addition for 4 years:

Year 2: $\$1050+50=\$1100$

Year 3: $\$1100+50=\$1150$

Year 4: $\$1150+50=\$1200$

Final amount after 4 years: $=\$1200$

$49\times 26$

We can round down and rewrite as:

$=(50\times 26)-(1\times 26)$

$=1300-26$

$=1274$

$102\times 17$

We can round up and rewrite as:

$=(100\times 17)+(2\times 17)$

$=1700+34$

$=1734$

$16\times 25$

We divide 16 by 2 and multiply 25 by 2 and rewrite as:

$=(16÷2)\times (25\times 2)$

$=8\times 50$

$=400$

$48\times 15$

We divide 48 by 2 and multiply 15 by 2 and rewrite as:

$=(48÷2)\times (15\times 2)$

$=24\times 30$

$=720$

$38\times 7$

Break the numbers into more manageable parts and rewrite as:

$=(30\times 7)+(8\times 7)$

$=210+56$

$=266$

$232\times 46$

Break the numbers down as much as you need to make the equation manageable. For example this equation can be broken down even further:

$=(200\times 46)+(30\times 46)+(2\times 46)$

$=(200\times 40)+(200\times 6)+(30\times 40+(30\times 6)+(2\times 46)$

$=8000+1200+1200+180+92$

$=\mathrm{10,672}$

$125÷5$

1. 5 does not go into 1, so move to next number
2. 5 goes 2 times into 12 (remainder 2)
3. Bring down 5, making it 25
4. 5 goes 5 times into 25
5. The quotient is 25

$=25$

$196÷7$

1. Recognize that 7 goes into 196 multiple times.
2. A large, easy multiple of 7 is 140 (since 7 × 20 = 140)
3. Subtract 140 from the dividend (196)
4. Find how many times 7 goes into 56
5. Add up the partial quotients

1. $196÷7$
2. $140=7\times 20$
3. $196-140=56$
4. $56=7\times 8$
5. $20+8$

$=28$

Solve $198÷4$ by estimation.

Round 198 to 200 to get an aproximate answer.

$200÷4$

$=50$ (aproximate answer)

$=49.5$ (exact answer)

Solve $20÷5$ using repeated subtraction.

Keep subtracting 5 until you reach 0. The number of times you subtract 5 is the quotient.

1. $20-5=15$
   
2. $15-5=10$
   
3. $10-5=5$
   
4. $5-5=0$

We subtracted 5 four times, therefore the quotient is:

$=4$